{"id":27398,"date":"2023-04-12T04:18:25","date_gmt":"2023-04-12T04:18:25","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=27398"},"modified":"2024-02-05T16:11:46","modified_gmt":"2024-02-05T16:11:46","slug":"solving-one-step-equations","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/one-step-equations","title":{"rendered":"Solving One-step Equations"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-fc461ab6-bee9-464d-abe8-7c111199f20d\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/one-step-equations#0-what-are-one-step-equations>What Are One-step Equations?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/one-step-equations#2-rules-for-one-step-algebraic-equations>Rules for One-step Algebraic Equations<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/one-step-equations#3-how-to-solve-one-step-equations>How to Solve One-step Equations<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/one-step-equations#6-solved-examples-on-one-step-equations>Solved Examples On One-Step Equations<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/one-step-equations#7-practice-problems-on-one-step-equations>Practice Problems On One-Step Equations<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/one-step-equations#8-frequently-asked-questions-on-one-step-equations>Frequently Asked Questions On One-Step Equations<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-one-step-equations\">What Are One-step Equations?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>One-step equations are algebraic equations that can be solved in one step only. <\/strong>They can be solved in just one step by isolating the variable using the inverse operations. An equation is a mathematical statement that shows that two mathematical expressions are equal.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The most basic and simple algebraic equations consist of one or more variables in math.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An equation consists of two sides, L.H.S. (Left Hand Side) and R.H.S. (Right hand Side) separated by \u201c=\u201d sign. Solving an equation simply means finding the value of the unknown variable.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider an equation.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x\\;-\\;7 = 93$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s add 7 on both sides to cancel out 7 and isolate the variable.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x\\;-\\;7 + 7 = 93 + 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $x = 100$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Wasn\u2019t that simple? This is what we call a \u201cone-step equation.\u201d<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Note:<\/strong> Take note of inverse operations that help in solving the one-step equations.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"356\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/One-Step-Algebraic-Equations-1.png\" alt=\"Inverse operations used to solve one-step equations\" class=\"wp-image-27404\" title=\"Inverse operations used to solve one-step equations\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/One-Step-Algebraic-Equations-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/One-Step-Algebraic-Equations-1-300x172.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-definition-of-one-step-equations\">Definition of One-step Equations<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>One-step equations are simple algebraic equations that can be solved in just one step.<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To solve one-step equations, we determine the value of the variable involved using different properties of equality. The operation you perform on one side of the equation must be carried out on the other side as well, in order to keep the equation balanced. One-step equations may involve integers, fractions, or decimals.&nbsp;<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-and-find-the-amount-of-money-in-given-word-problems\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/measurement_add_word_prob_2_pt.png\" alt=\"Add and Find the Amount of Money in Given Word Problems Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add and Find the Amount of Money in Given Word Problems Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-by-regrouping-ones-and-tens\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_regrp_ones_tens_vertical_pt.png\" alt=\"Add by Regrouping Ones and Tens Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add by Regrouping Ones and Tens Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-by-regrouping-ones\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_regrp_ones_vertical_pt.png\" alt=\"Add by Regrouping Ones Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add by Regrouping Ones Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-by-regrouping-the-ones\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_regrp_ones_horizontal_pt.png\" alt=\"Add by Regrouping the Ones Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add by Regrouping the Ones Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-money\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/money_add_money_amounts_pt.png\" alt=\"Add Money Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Money Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-ones-to-a-2-digit-number-using-place-value\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_column_add_3_pt.png\" alt=\"Add Ones to a 2-digit Number using Place Value Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Ones to a 2-digit Number using Place Value Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-ones-to-a-2-digit-number-using-visuals\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_base_10_blocks_3_pt.png\" alt=\"Add Ones to a 2-digit Number using Visuals Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Ones to a 2-digit Number using Visuals Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-the-given-amounts-of-money\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/money_add_money_pt.png\" alt=\"Add the Given Amounts of Money Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add the Given Amounts of Money Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/adding-one-by-making-a-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_model_add_1_pt.png\" alt=\"Adding One by Making a Model Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Adding One by Making a Model Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/arrange-coins-and-count-money\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/money_arrange_count_pnd_g1_pt.png\" alt=\"Arrange Coins and Count Money Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Arrange Coins and Count Money Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    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to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-rules-for-one-step-algebraic-equations\">Rules for One-step Algebraic Equations<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">While keeping the equation balanced on both sides, the subsequent operations are carried out to isolate the variable. By doing this, LHS continues to be equal to RHS, and eventually, the balance is maintained. There are some rules for one-step algebraic equations. They are as follows:<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">One-step Equation with Addition&nbsp;<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If the equation involves addition, we can isolate the variable using the inverse operation, which is the subtraction operation.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we subtract the same number from both sides of an equation, both sides will remain equal. This is the subtraction property of equality.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x + 5 = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow x + 5\\;-\\;5 = 2\\;-\\;5$ \u2026subtract 5 from both sides<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow x =\\;-\\;3$<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">One-step Equation with Subtraction<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If the equation involves subtraction, we isolate the variable using the addition property of equality.<strong> <\/strong>If we add the same number to both sides of an equation, both sides will remain equal.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$c\\;-\\;1.1&nbsp;= 12$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow c\\;-\\;1.1 + 1.1 = 12 + 1.1$ \u2026adding 1.1 on both sides<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow c = 13.1$<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">One-step Equation with Multiplication<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If the equation involves multiplication, we can isolate the variable using division. However, note that we cannot divide by 0.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we divide both sides of an equation by the same number, both sides will remain equal.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4x = 16$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{4x}{4}&nbsp; = \\frac{16}{4}$ \u2026divide both sides by 4<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow x = 4$<\/p>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">One-step Equation with Division<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If the equation involves division, we use multiplication to solve the equation.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we multiply both sides of an equation by the same number, both sides will remain equal.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{x}{4} = \\frac{1}{5}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{x}{4} \\times 4 = \\frac{1}{5}\\times4$ \u2026 multiply both sides by 4<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = \\frac{4}{5}$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"544\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/One-Step-Algebraic-Equations-2.png\" alt=\"One-step equation: rules and examples\" class=\"wp-image-27405\" title=\"One-step equation: rules and examples\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/One-Step-Algebraic-Equations-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/One-Step-Algebraic-Equations-2-300x263.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-subtract-ones-2-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-subtract-ones-2-digit-numbers.jpeg\" alt=\"Add & Subtract Ones & 2-Digit Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-3-digit-and-1-digit-numbers-with-regrouping-ones-and-tens-horizontal-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-3-digit-and-1-digit-numbers-with-regrouping-ones-and-tens-horizontal-addition.jpeg\" alt=\"Add 3 Digit and 1 Digit Numbers with Regrouping Ones and Tens: Horizontal Addition\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a 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data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-money-to-write-the-total-amount.jpeg\" alt=\"Add Money to Write the Total Amount Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = 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slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-how-to-solve-one-step-equations\">How to Solve One-step Equations<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When you\u2019re solving one-step algebraic equations, the goal is to get the variable on one side and all the remaining numbers on the other. We use the inverse operation or the opposite operation to the operation acting on the variable. The inverse operations pairwise are addition and subtraction and division and multiplication.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The steps to solve one-step equations are as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 1: Note down the equation.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example $x\\;-\\;5 = 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An equation will have a variable (x), which denotes an unknown value, and it will also have a constant, which is a number you need to add or subtract from the variable to equal a certain sum or difference.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 2: Isolate the variable.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">You must conduct an inverse operation to cancel the constants in order to isolate a variable, on one side of the equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, in the equation, $x \\;-\\; 5 = 10 , 5$&nbsp; is subtracted from the variable, so to isolate the variable you must cancel the 5 by adding it on both sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 3: Adding or subtracting the constant from both sides.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">While solving the equation, we have to keep both sides balanced.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, if you need to add a value to isolate the variable, you must also add that same value to the other side of the equation, also if you need to subtract a value on one side of the equation you have to subtract it from the other side.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the equation, $x \\;-\\; 5 = 10$, we need to add 5 on the left as well as on the right.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x \\;-\\; 5 + 5 = 10 + 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $x = 15$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 4: Verify your solution.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To verify the solution, simply plug in the value of x in the equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x \\;-\\; 5 = 10$, the value of x as we found out is 15.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, substituting the value, the equation becomes, $15 \\;-\\; 5 = 10$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since this equation is true, your solution is correct.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Similarly, if the variable is multiplied by a number, divide both sides of the equation by the same number to isolate the variable. (If the variable is divided by a number, multiply both sides of the equation by the same number.)&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, let\u2019s solve an equation.&nbsp; $\\frac{x}{6} = 12$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">As the variable is divided by 6, to isolate it, you need to multiply by 6.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$6(\\frac{x}{6}) = 12\\times6$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow x &nbsp; = 72$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Verifying the solution, as&nbsp; $\\frac{72}{6}&nbsp; = 12$ , the solution is correct.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-facts-about-one-step-equations\">Facts about One-step Equations<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">A one-step equation is an equation that requires only one step to solve.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The most common one-step equations are linear algebraic equations.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When solving an equation, you may keep the variable on either side of the equation. As long as in the end, the variable that you are solving is isolated on one side with a coefficient of $+1$.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we have learned how to solve one-step equations, its rules and the steps of solving the equations. Let\u2019s now solve some examples to better understand the concept.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-solved-examples-on-one-step-equations\">Solved Examples On One-Step Equations<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Solve this equation with a negative constant: <\/strong>$\\;-\\;8 + x = 14$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution: <\/strong>Since the constant is negative, adding it to both sides will isolate the variable.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow -8 + x = 14$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow -8 + x + 8 = 14 + 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = 22$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Verifying the solution, $-8 + 22 = 14$. The solution is correct.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. Solve this equation with a negative coefficient:&nbsp; <\/strong>$-4x = 32$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since the variable is multiplied by $-4$, to isolate the variable, you must divide each side by $-4$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Remember that dividing a positive number by a negative number equals a negative quotient.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$-4x = 32$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{-4x}{-4} = \\frac{32}{-4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow x = \\;-\\; 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Verifying the solution, $-4(\\;-8) = 32$. The solution is correct.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. Jennifer weighed herself on the scale and found her weight to be 120 lbs. Then, she held the cat and stepped on the scale and found the combined weight to be 132 lbs.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Create an equation that models the situation and solve the equation to find c, the cat\u2019s weight.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> To model the following situation, we will create an equation to show the combined &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; weights of Jennifer and cat.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$c + 120 = 132$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To solve for c, we will do the inverse operation of addition and subtract 120 from each side:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$c + 120 \\;-\\; 120 = 132 \\;-\\; 120$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow c = 12$ lbs.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To verify answer we will plug in the values in the equation<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$12 + 120 = 132$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, $c = 12$ lbs is the correct solution.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Solve the equation: <\/strong>$10 = \\frac{p}{10}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> Since the variable is divided by 10, we have to isolate it by multiplying it by 10.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$10 = \\frac{p}{10}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow 10\\times10 = \\frac{p}{10}\\times10$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow P = 100$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Verifying the solution, $10 = \\frac{100}{10}$ . The solution is correct.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-practice-problems-on-one-step-equations\">Practice Problems On One-Step Equations<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Solving One-step Equations<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the value of x in the equation $5x = 40$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">45<\/div><div class=\"spq_answer_block\" data-value=\"1\">8<\/div><div class=\"spq_answer_block\" data-value=\"2\">6<\/div><div class=\"spq_answer_block\" data-value=\"3\">35<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 8<br\/>We will isolate the variable by dividing both sides of the equation by the same number, both sides will remain equal and we will get the solution.\r\nFor example,$\\frac{5x}{5}  = \\frac{40}{5}$ .Thus,  $x = 8$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Identify the equation, where the value of $z = 7$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5z = 15<\/div><div class=\"spq_answer_block\" data-value=\"1\">6z = 36<\/div><div class=\"spq_answer_block\" data-value=\"2\">8z = 32<\/div><div class=\"spq_answer_block\" data-value=\"3\">4z = 28<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 4z = 28<br\/>We will isolate the variable by dividing both sides of the equation by the same number. $\\frac{4z}{4} = \\frac{28}{4}$  Thus, $z = 7$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Identify the equation that does not have a solution at $w = 5$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">w $+ 7 = 12$<\/div><div class=\"spq_answer_block\" data-value=\"1\">w $\\;\u2013\\; 5 = 10$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$6 +$ w $= 11$<\/div><div class=\"spq_answer_block\" data-value=\"3\">w $\u2013\\; 4 = 1$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: w $\\;\u2013\\; 5 = 10$<br\/>Substituting the value in equation, w $-\\; 5 = 10$<br>\r\n$5 \\;-\\; 5 = 10$, which is a false statement.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What equation matches this situation?<br>Maria had some pencils then bought 4 more. Now she has a total of 10 pencils.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$P\\; \u2013\\; 4 = 10$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$10 + 4 = P$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$P + 4 = 10$<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $P + 4 = 10$<br\/>Let's consider pencil as p, Maria has p number of pencils, and she bought 4 more,<br>\r\ni.e., $P + 4$. Now she has a total of ten pencils, which means $P + 4 = 10$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">What is the first step to solve this equation:  $2x = 18$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Add 2 to both sides.<\/div><div class=\"spq_answer_block\" data-value=\"1\">Subtract 2 from both sides.<\/div><div class=\"spq_answer_block\" data-value=\"2\">Multiply by 3 on both sides.<\/div><div class=\"spq_answer_block\" data-value=\"3\">Divide by 2 on both sides.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Divide by 2 on both sides.<br\/>In the equation above, x is being multiplied by 2. Thus, to isolate the equation, we have to do the inverse and divide both sides of the equation by 2.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Solving One-step Equations\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Solving One-step Equations\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the value of x in the equation $$5x = 40$$?\",\n                    \"text\": \"What is the value of x in the equation $$5x = 40$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We will isolate the variable by dividing both sides of the equation by the same number, both sides will remain equal and we will get the solution.\r\nFor example,$$\\\\frac{5x}{5}  = \\\\frac{40}{5}$$ .Thus,  $$x = 8$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"45\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will isolate the variable by dividing both sides of the equation by the same number, both sides will remain equal and we will get the solution.\r\nFor example,$$\\\\frac{5x}{5}  = \\\\frac{40}{5}$$ .Thus,  $$x = 8$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will isolate the variable by dividing both sides of the equation by the same number, both sides will remain equal and we will get the solution.\r\nFor example,$$\\\\frac{5x}{5}  = \\\\frac{40}{5}$$ .Thus,  $$x = 8$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"35\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will isolate the variable by dividing both sides of the equation by the same number, both sides will remain equal and we will get the solution.\r\nFor example,$$\\\\frac{5x}{5}  = \\\\frac{40}{5}$$ .Thus,  $$x = 8$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We will isolate the variable by dividing both sides of the equation by the same number, both sides will remain equal and we will get the solution.\r\nFor example,$$\\\\frac{5x}{5}  = \\\\frac{40}{5}$$ .Thus,  $$x = 8$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We will isolate the variable by dividing both sides of the equation by the same number, both sides will remain equal and we will get the solution.\r\nFor example,$$\\\\frac{5x}{5}  = \\\\frac{40}{5}$$ .Thus,  $$x = 8$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify the equation, where the value of $$z = 7$$.\",\n                    \"text\": \"Identify the equation, where the value of $$z = 7$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We will isolate the variable by dividing both sides of the equation by the same number. $$\\\\frac{4z}{4} = \\\\frac{28}{4}$$  Thus, $$z = 7$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5z = 15\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will isolate the variable by dividing both sides of the equation by the same number. $$\\\\frac{4z}{4} = \\\\frac{28}{4}$$  Thus, $$z = 7$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6z = 36\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will isolate the variable by dividing both sides of the equation by the same number. $$\\\\frac{4z}{4} = \\\\frac{28}{4}$$  Thus, $$z = 7$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8z = 32\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will isolate the variable by dividing both sides of the equation by the same number. $$\\\\frac{4z}{4} = \\\\frac{28}{4}$$  Thus, $$z = 7$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"4z = 28\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We will isolate the variable by dividing both sides of the equation by the same number. $$\\\\frac{4z}{4} = \\\\frac{28}{4}$$  Thus, $$z = 7$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We will isolate the variable by dividing both sides of the equation by the same number. $$\\\\frac{4z}{4} = \\\\frac{28}{4}$$  Thus, $$z = 7$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify the equation that does not have a solution at $$w = 5$$.\",\n                    \"text\": \"Identify the equation that does not have a solution at $$w = 5$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Substituting the value in equation, w $$-\\\\; 5 = 10$$<br>\r\n$$5 \\\\;-\\\\; 5 = 10$$, which is a false statement.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"w $$+ 7 = 12$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Substituting the value in equation, w $$-\\\\; 5 = 10$$<br>\r\n$$5 \\\\;-\\\\; 5 = 10$$, which is a false statement.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$6 +$$ w $$= 11$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Substituting the value in equation, w $$-\\\\; 5 = 10$$<br>\r\n$$5 \\\\;-\\\\; 5 = 10$$, which is a false statement.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"w $$\u2013\\\\; 4 = 1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Substituting the value in equation, w $$-\\\\; 5 = 10$$<br>\r\n$$5 \\\\;-\\\\; 5 = 10$$, which is a false statement.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"w $$\\\\;\u2013\\\\; 5 = 10$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Substituting the value in equation, w $$-\\\\; 5 = 10$$<br>\r\n$$5 \\\\;-\\\\; 5 = 10$$, which is a false statement.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Substituting the value in equation, w $$-\\\\; 5 = 10$$<br>\r\n$$5 \\\\;-\\\\; 5 = 10$$, which is a false statement.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What equation matches this situation?<br>Maria had some pencils then bought 4 more. Now she has a total of 10 pencils.\",\n                    \"text\": \"What equation matches this situation?<br>Maria had some pencils then bought 4 more. Now she has a total of 10 pencils.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Let's consider pencil as p, Maria has p number of pencils, and she bought 4 more,<br>\r\ni.e., $$P + 4$$. Now she has a total of ten pencils, which means $$P + 4 = 10$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$P\\\\; \u2013\\\\; 4 = 10$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let's consider pencil as p, Maria has p number of pencils, and she bought 4 more,<br>\r\ni.e., $$P + 4$$. Now she has a total of ten pencils, which means $$P + 4 = 10$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$10 + 4 = P$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let's consider pencil as p, Maria has p number of pencils, and she bought 4 more,<br>\r\ni.e., $$P + 4$$. Now she has a total of ten pencils, which means $$P + 4 = 10$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let's consider pencil as p, Maria has p number of pencils, and she bought 4 more,<br>\r\ni.e., $$P + 4$$. Now she has a total of ten pencils, which means $$P + 4 = 10$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$P + 4 = 10$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Let's consider pencil as p, Maria has p number of pencils, and she bought 4 more,<br>\r\ni.e., $$P + 4$$. Now she has a total of ten pencils, which means $$P + 4 = 10$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Let's consider pencil as p, Maria has p number of pencils, and she bought 4 more,<br>\r\ni.e., $$P + 4$$. Now she has a total of ten pencils, which means $$P + 4 = 10$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the first step to solve this equation:  $$2x = 18$$.\",\n                    \"text\": \"What is the first step to solve this equation:  $$2x = 18$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"In the equation above, x is being multiplied by 2. Thus, to isolate the equation, we have to do the inverse and divide both sides of the equation by 2.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Add 2 to both sides.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the equation above, x is being multiplied by 2. Thus, to isolate the equation, we have to do the inverse and divide both sides of the equation by 2.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Subtract 2 from both sides.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the equation above, x is being multiplied by 2. Thus, to isolate the equation, we have to do the inverse and divide both sides of the equation by 2.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Multiply by 3 on both sides.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the equation above, x is being multiplied by 2. Thus, to isolate the equation, we have to do the inverse and divide both sides of the equation by 2.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Divide by 2 on both sides.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In the equation above, x is being multiplied by 2. Thus, to isolate the equation, we have to do the inverse and divide both sides of the equation by 2.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In the equation above, x is being multiplied by 2. Thus, to isolate the equation, we have to do the inverse and divide both sides of the equation by 2.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-frequently-asked-questions-on-one-step-equations\">Frequently Asked Questions On One-Step Equations<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-982fa10a-0e7b-479e-b380-5d339ad0a812\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-982fa10a-0e7b-479e-b380-5d339ad0a812\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-982fa10a-0e7b-479e-b380-5d339ad0a812\"><strong>What are the various methods for solving equations?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-982fa10a-0e7b-479e-b380-5d339ad0a812\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">There are three methods used to solve systems of equations. They are as follows:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">&nbsp;&nbsp;Graphing<\/li>\n\n\n\n<li class=\"eplus-wrapper\">&nbsp;&nbsp;Substitution<\/li>\n\n\n\n<li class=\"eplus-wrapper\">&nbsp;&nbsp;Elimination<\/li>\n<\/ul>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-982fa10a-0e7b-479e-b380-5d339ad0a812\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-982fa10a-0e7b-479e-b380-5d339ad0a812\"><strong>What is the difference between one-step equations and two-step equations?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-982fa10a-0e7b-479e-b380-5d339ad0a812\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">One-step equations require only one step, one inverse operation to be solved and have only one operation. Two-step equations require two inverse operations to solve and have two operations.For eg., $x^2 = 64$ is a one-step equation, while $3x + 2 = 14$ is a two-step equation.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-982fa10a-0e7b-479e-b380-5d339ad0a812\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-982fa10a-0e7b-479e-b380-5d339ad0a812\"><strong>What are linear equations in one variable?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-982fa10a-0e7b-479e-b380-5d339ad0a812\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A linear equation in one variable is an equation in which the degree of the variable is 1. These are also known as first degree equations, because the highest exponent on the variable is 1. All linear equations eventually can be written in the form $ax + b = c$, where a, b, and c are real numbers and $a \\neq 0$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-982fa10a-0e7b-479e-b380-5d339ad0a812\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-982fa10a-0e7b-479e-b380-5d339ad0a812\"><strong>What is a one-solution equation?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-982fa10a-0e7b-479e-b380-5d339ad0a812\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Some equations have exactly one solution. In these equations, there is only one value for the variable that makes the equation true. You can tell that an equation has one solution if you solve the equation and get a variable equal to a number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For eg., $5x = 25$ has a variable term, $5x$ on one side of the equation and a constant term, 25, on the other side of the equation. So, it has one solution. Let&#8217;s solve the equation to see why.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$5x = 25$&nbsp; . Divide both sides by 5.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;$x = 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So,&nbsp;$5x = 25$&nbsp; has one solution, $x = 5$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-982fa10a-0e7b-479e-b380-5d339ad0a812\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-982fa10a-0e7b-479e-b380-5d339ad0a812\"><strong>What are equations with no solutions?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-982fa10a-0e7b-479e-b380-5d339ad0a812\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If a linear equation has the same variable term but different constant values on opposite sides of the equation, it has no solutions.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For eg., $2x + 4 = 1 + 2x$ has the same variable term, $2x$, but different constant terms, 4 and 1, on opposite sides of the equation. So, it has no solutions. Let\u2019s solve the equation to see why.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$2x + 4 = 1 + 2x$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Subtract 2x from both sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4 = 1$The statement $4 = 1$ is false. So, $2x + 4 = 1 + 2x$ has no solutions.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are One-step Equations? One-step equations are algebraic equations that can be solved in one step only. They can be solved in just one step by isolating the variable using the inverse operations. An equation is a mathematical statement that shows that two mathematical expressions are equal.&nbsp; The most basic and simple algebraic equations consist &#8230; <a title=\"Solving One-step Equations\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/one-step-equations\" aria-label=\"More on Solving One-step Equations\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-27398","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27398","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=27398"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27398\/revisions"}],"predecessor-version":[{"id":39960,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27398\/revisions\/39960"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=27398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=27398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=27398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}