{"id":1165,"date":"2022-04-14T10:15:18","date_gmt":"2022-04-14T10:15:18","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1165"},"modified":"2023-02-14T15:42:31","modified_gmt":"2023-02-14T15:42:31","slug":"inequality-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/counting-and-comparison\/inequality","title":{"rendered":"Inequality &#8211; Definition with Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><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-ab41e170-f43b-4d08-bf7b-f6674a220f3a\" 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\/counting-and-comparison\/inequality#0-origin-of-the-term-inequality>Origin of the Term: Inequality<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/counting-and-comparison\/inequality#1-lets-look-at-the-rules-of-inequalities>Let&#8217;s Look at the Rules of Inequalities<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/counting-and-comparison\/inequality#2-real-life-example-of-inequality>Real life Example of Inequality<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/counting-and-comparison\/inequality#3-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/counting-and-comparison\/inequality#4-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/counting-and-comparison\/inequality#5-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<p class=\" eplus-wrapper\">In mathematics, a relationship between two expressions or values that are not equal to each other is called <strong>\u2018inequality<\/strong>.\u2019 So, a lack of balance results in inequality. For example, if you want to buy a new bicycle that costs $250, but you have $225. It is also an inequality as you are comparing two numbers that aren&#8217;t equal.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">We use \u2018=\u2019 when two quantities are equal and when they are not equal we use the symbol \u2260 to denote not equal. If two things are not equal, the first value can be either greater than (&gt;) or lesser than (&lt;) or greater than equal to (\u2265) or less than equal to (\u2264) the second value. So, as per the above example, $250&nbsp; &gt; $225.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-1.png\" alt=\"inequalities explained by mathematics signs\" class=\"wp-image-5404\" title=\"inequalities explained by mathematics signs\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-1-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">In Mathematics,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"497\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-2.png\" alt=\"Mathematics symbol and their meaning with examples\" class=\"wp-image-5405\" title=\"Mathematics symbol and their meaning with examples\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-2-300x240.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"429\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-3.png\" alt=\"fun fact about inequalities.\" class=\"wp-image-5406\" title=\"fun fact about inequalities.\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-3-300x208.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"0-origin-of-the-term-inequality\">Origin of the Term: Inequality<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">The term \u2018inequality\u2019 comes from the Old French word <em>inequalit\u00e9 <\/em>and the Latin word <em>inequalitas, <\/em>meaning \u2018unequal, unlike, different\u2019 and changeable. This term is used to compare the magnitude, number, and intensity of two values or expressions.<\/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\/applications-of-skip-counting\" 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\/count_comp_skip100_application_problem_pt.png\" alt=\"Applications of Skip Counting 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\">Applications of Skip Counting 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\/apply-skip-counting-in-real-world\" 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\/count_comp_skip10_application_problem_pt.png\" alt=\"Apply Skip Counting in Real World 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\">Apply Skip Counting in Real World 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\/choose-the-next-number-in-the-counting-sequence\" 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\/count_comp_count_forward_w5_pt.png\" alt=\"Choose the Next Number in the Counting Sequence 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\">Choose the Next Number in the Counting Sequence 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\/click-on-the-next-number-in-the-counting-sequence\" 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\/count_comp_sequence_1_w10_pt.png\" alt=\"Click on the Next Number in the Counting Sequence 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\">Click on the Next Number in the Counting Sequence 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\/click-the-correct-number-after-counting\" 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\/count_comp_scttrd_objs_w10_pt.png\" alt=\"Click the Correct Number after Counting 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\">Click the Correct Number after Counting 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\/compare-by-counting\" 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\/count_comp_treehouse_party_8_9_gm.png\" alt=\"Compare by Counting 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\">Compare by Counting 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\/complete-the-comparison\" 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\/count_comp_compare_find_number_pt.png\" alt=\"Complete the Comparison 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\">Complete the Comparison 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\/complete-the-counting-sequence\" 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\/count_comp_missing_numbers_w5_pt.png\" alt=\"Complete the Counting Sequence 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\">Complete the Counting Sequence 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\/complete-the-skip-counting-sequence\" 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\/count_comp_skip5_complete_pattern_2_pt.png\" alt=\"Complete the Skip Counting Sequence 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\">Complete the Skip Counting Sequence 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\/counting-by-10s\" 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\/count_comp_skip_count_10_next_number_pt.png\" alt=\"Counting by 10s 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\">Counting by 10s 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                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = 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=\"eplus-wrapper wp-block-heading\" id=\"1-lets-look-at-the-rules-of-inequalities\">Let&#8217;s Look at the Rules of Inequalities<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"292\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-4.png\" alt=\"Rules of Inequalities\" class=\"wp-image-5407\" title=\"Rules of Inequalities\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-4.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-4-300x141.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Rule 1:<\/strong> When inequalities are linked, you can jump across them. So, if <em>a<\/em> is greater than <em>b<\/em>, and <em>b<\/em> is greater than <em>c<\/em>, <em>a<\/em> will also be greater than <em>c<\/em>.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">If <em>a<\/em> &gt; <em>b<\/em> &gt; <em>c<\/em>, <em>a<\/em> &gt; <em>c<\/em>, we can jump over b to find out the relation between a and c directly.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Example: If you (5) have more pens than Mia (3), and Mia (3) has more pens than Benj (1), then you (5) automatically have more pens than Benj (1).<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Rule 2:<\/strong>&nbsp; If you exchange the values, the sign also reverses.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">If <em>p<\/em> &gt; <em>q<\/em>, then <em>q<\/em> &lt; <em>p<\/em><\/li>\n\n\n\n<li class=\" eplus-wrapper\">If <em>p<\/em> &lt; <em>q<\/em>, then <em>q<\/em> &gt; <em>p<\/em><\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\">Example: If Mia is taller than Ben, then Ben will be shorter than Mia.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Rule 3<\/strong>: An inequality can either be &gt; or &lt; but never both at the same time.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">If <em>x<\/em> &gt; <em>y<\/em>, then it is impossible to have an equation <em>x<\/em> &lt; <em>y<\/em> at the same time<\/li>\n\n\n\n<li class=\" eplus-wrapper\">If <em>x<\/em> &lt; <em>y<\/em>, then it is impossible to have an equation <em>x<\/em> &gt; <em>y<\/em> at the same time<\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\">Either <em>x<\/em> will be greater than <em>y<\/em> or less than <em>y<\/em> but not both.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Example: If Weight of Ball 1 &gt; Weight of a Ball 2, then it is not possible that Weight of Ball 1 &lt; Weight of Ball 2 at the same time.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Rule 4<\/strong>: Multiplying both sides of the inequality by a negative sign, reverses the sign.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">If <em>p<\/em> &gt; <em>q<\/em>, then \u2212<em>p<\/em> &lt; \u2212<em>q&nbsp;<\/em><\/li>\n\n\n\n<li class=\" eplus-wrapper\">If <em>p<\/em> &lt; <em>q<\/em>, then \u2212<em>p<\/em> &gt; \u2212<em>q<\/em><\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\">Example: 3 &gt; 2, but \u22123 &lt; \u22122 in mathematics.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Rule 5:<\/strong> Taking a reciprocal also changes the direction of the inequality.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">If <em>p<\/em> &gt; <em>q<\/em>, then $\\frac{1}{p}$ &lt; $\\frac{1}{q}$<\/li>\n\n\n\n<li class=\" eplus-wrapper\">If <em>p<\/em> &lt; <em>q<\/em>, then $\\frac{1}{p}$ &gt; $\\frac{1}{q}$<\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\">Example: 5 &gt; 3 but, $\\frac{1}{5}$ &lt; $\\frac{1}{3}$ in mathematics.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Rule 6:<\/strong> Adding or subtracting the same quantity to each side of the inequality, does not change the inequality sign.&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">If <em>p<\/em> &gt; <em>q<\/em>, then <em>p + r<\/em> &gt; <em>q + r&nbsp;<\/em><\/li>\n\n\n\n<li class=\" eplus-wrapper\">If <em>p<\/em> &lt; <em>q<\/em>, then <em>p &#8211; r <\/em>&nbsp;&lt; <em>q &#8211; r<\/em><\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Rule 7:<\/strong> Dividing or multiplying by a positive quantity on each side of the inequality, does not change the inequality sign.&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">If <em>p<\/em> &gt; <em>q<\/em>, then pr &gt; qr<em>&nbsp;<\/em><\/li>\n\n\n\n<li class=\" eplus-wrapper\">If <em>p<\/em> &lt; <em>q<\/em>, then&nbsp; <em>pr<\/em> &lt; <em>qr<\/em><\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\">Example: 5 &gt; 3 but, $\\frac{1}{5}$ &lt; $\\frac{1}{3}$ in mathematics.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Rule 8:<\/strong> Dividing by a negative quantity on each side of the inequality, reverses the sign.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">If <em>p<\/em> &gt; <em>q<\/em>, then $\\frac{p}{-r}$ &lt; $\\frac{q}{-r}$<em> <\/em>&nbsp;<\/li>\n\n\n\n<li class=\" eplus-wrapper\">If <em>p<\/em> &lt; <em>q<\/em>, then $\\frac{p}{-r}$ &gt; $\\frac{q}{-r}$<em> <\/em>&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\">These rules of inequalities help us find the solutions of the inequalities.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Graphical representation of inequalities<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"521\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-5.png\" alt=\"Graphical representation of inequalities\" class=\"wp-image-5408\" title=\"Graphical representation of inequalities\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-5.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Inequality-5-300x252.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">We use an empty circle to show that the limit value is not the solution to the given inequality.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Filled circle is used to show that the limit value is the solution of the given inequality.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Extending an arrow to the right end (if greater than) or left (if less than) signifies all the values the variable can take.<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div 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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 = slidesContainer.querySelectorAll(\".worksheet-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                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = 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=\"eplus-wrapper wp-block-heading\" id=\"2-real-life-example-of-inequality\">Real life Example of Inequality<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Speed limit on the road is 30 mph which can be expressed by the inequality:<\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\">Speed \u2264 30 mph<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Maximum capacity of a container is 5 liters.<\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\">Volume \u2264 5 <em>l<\/em><\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Children should not be less than 4 feet to ride the roller coaster.<\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\">Child\u2019s height &gt; 4 feet<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Plane has to fly at 500 m above sea level or higher.<\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\">Plane flying level $\\ge$500 m<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Credit card limit per month is $5,000.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\">Money that can be spent in month \u2264 $5,000<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"3-solved-examples\">Solved Examples<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\"><strong>Given the conditions X &gt; 30 and Y &gt; X; which is the largest quantity?<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Y is the largest quantity as Y &gt; X &gt; 30.<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\"><strong>Determine the relation of <\/strong>$\\frac{1}{x}$ and $\\frac{1}{y}$ if <em>x<\/em> &gt; <em>y<\/em>.<\/li>\n<\/ol>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Since signs change in reciprocals, the equation will be $\\frac{1}{x}$&nbsp; &lt; $\\frac{1}{y}$.<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\"><strong>Determine the relation of \u2212<\/strong><strong><em>a<\/em><\/strong><strong> and \u2212<\/strong><strong><em>b<\/em><\/strong><strong> if a \uff1c b.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\" eplus-wrapper\">Multiplying by a negative number (-1 in this case) reverses the sign.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">So, \u2212<em>a <\/em>&gt; \u2212<em>b<\/em><\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"4-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Inequality<\/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\">Which of the following value satisfy the inequality?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">3<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">5<\/div><div class=\"spq_answer_block\" data-value=\"3\">4<\/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: 2<br\/>5 - x =  5 \u2212 2 = 3\r\n3 \u2265 3<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Identify the correct solution set for the inequality: \u2018x is greater than or equal to 15.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">0, 12, 16<\/div><div class=\"spq_answer_block\" data-value=\"1\">15, 16, 17<\/div><div class=\"spq_answer_block\" data-value=\"2\">14, 15, 16<\/div><div class=\"spq_answer_block\" data-value=\"3\">4, 5, 6<\/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: 15, 16, 17<br\/>Given inequality is x \u2265 15.\r\nSo all the numbers should be either greater than or equal to 15.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Determine the correct inequality symbol between the given expressions:<br> (5 + 3) and (1 + 8)<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">(5 + 3) $\\lt$ (1 + 8)<\/div><div class=\"spq_answer_block\" data-value=\"1\">(5 + 3) $\\ge$ (1 + 8)<\/div><div class=\"spq_answer_block\" data-value=\"2\">(5 + 3) $\\gt$ (1 + 8)<\/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: (5 + 3) $\\lt$ (1 + 8)<br\/>Here, first we have to solve both the expressions.<br>\r\n5 + 3 = 8<br>\r\n1 + 8 = 9<br>\r\nNow, we know that 8 $\\lt$ 9. So, (5 + 3) $\\lt$ (1 + 8).<\/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\">Choose the correct graph that best describes numbers greater than 0.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">A<img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Practice-Problems-4-a.png\" alt=\"A\"><\/div><div class=\"spq_answer_block\" data-value=\"1\">B<img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Practice-Problems-4-b.png\" alt=\"B\"><\/div><div class=\"spq_answer_block\" data-value=\"2\">C<img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Practice-Problems-4-Correct-Answer-c.png\" alt=\"C\"><\/div><div class=\"spq_answer_block\" data-value=\"3\">D<img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Practice-Problems-4-d.png\" alt=\"D\"><\/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: C<br\/>The number is greater than 0. x > 0 so, 0 is the limit value and it is not the solution of given inequality hence an open circle. The variable can take any value greater than 0 so we extend an arrow to the right.<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Practice-Problems-4-c.png\"><\/div><\/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\": \"Inequality\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Inequality\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following value satisfy the inequality?\",\n                    \"text\": \"Which of the following value satisfy the inequality?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"5 - x =  5 \u2212 2 = 3\r\n3 \u2265 3\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"5 - x =  5 \u2212 2 = 3\r\n3 \u2265 3\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"5 - x =  5 \u2212 2 = 3\r\n3 \u2265 3\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"5 - x =  5 \u2212 2 = 3\r\n3 \u2265 3\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"2\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"5 - x =  5 \u2212 2 = 3\r\n3 \u2265 3\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"5 - x =  5 \u2212 2 = 3\r\n3 \u2265 3\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify the correct solution set for the inequality: \u2018x is greater than or equal to 15.\",\n                    \"text\": \"Identify the correct solution set for the inequality: \u2018x is greater than or equal to 15.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Given inequality is x \u2265 15.\r\nSo all the numbers should be either greater than or equal to 15.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0, 12, 16\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given inequality is x \u2265 15.\r\nSo all the numbers should be either greater than or equal to 15.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"14, 15, 16\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given inequality is x \u2265 15.\r\nSo all the numbers should be either greater than or equal to 15.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4, 5, 6\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given inequality is x \u2265 15.\r\nSo all the numbers should be either greater than or equal to 15.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"15, 16, 17\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Given inequality is x \u2265 15.\r\nSo all the numbers should be either greater than or equal to 15.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Given inequality is x \u2265 15.\r\nSo all the numbers should be either greater than or equal to 15.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Determine the correct inequality symbol between the given expressions:<br> (5 + 3) and (1 + 8)\",\n                    \"text\": \"Determine the correct inequality symbol between the given expressions:<br> (5 + 3) and (1 + 8)\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Here, first we have to solve both the expressions.<br>\r\n5 + 3 = 8<br>\r\n1 + 8 = 9<br>\r\nNow, we know that 8 $$\\\\lt$$ 9. So, (5 + 3) $$\\\\lt$$ (1 + 8).\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"(5 + 3) $$\\\\ge$$ (1 + 8)\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Here, first we have to solve both the expressions.<br>\r\n5 + 3 = 8<br>\r\n1 + 8 = 9<br>\r\nNow, we know that 8 $$\\\\lt$$ 9. So, (5 + 3) $$\\\\lt$$ (1 + 8).\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"(5 + 3) $$\\\\gt$$ (1 + 8)\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Here, first we have to solve both the expressions.<br>\r\n5 + 3 = 8<br>\r\n1 + 8 = 9<br>\r\nNow, we know that 8 $$\\\\lt$$ 9. So, (5 + 3) $$\\\\lt$$ (1 + 8).\"\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\": \"Here, first we have to solve both the expressions.<br>\r\n5 + 3 = 8<br>\r\n1 + 8 = 9<br>\r\nNow, we know that 8 $$\\\\lt$$ 9. So, (5 + 3) $$\\\\lt$$ (1 + 8).\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"(5 + 3) $$\\\\lt$$ (1 + 8)\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Here, first we have to solve both the expressions.<br>\r\n5 + 3 = 8<br>\r\n1 + 8 = 9<br>\r\nNow, we know that 8 $$\\\\lt$$ 9. So, (5 + 3) $$\\\\lt$$ (1 + 8).\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Here, first we have to solve both the expressions.<br>\r\n5 + 3 = 8<br>\r\n1 + 8 = 9<br>\r\nNow, we know that 8 $$\\\\lt$$ 9. So, (5 + 3) $$\\\\lt$$ (1 + 8).\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Choose the correct graph that best describes numbers greater than 0.\",\n                    \"text\": \"Choose the correct graph that best describes numbers greater than 0.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The number is greater than 0. x > 0 so, 0 is the limit value and it is not the solution of given inequality hence an open circle. The variable can take any value greater than 0 so we extend an arrow to the right.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Practice-Problems-4-a.png\\\"\/>\",\n                                \n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The number is greater than 0. x > 0 so, 0 is the limit value and it is not the solution of given inequality hence an open circle. The variable can take any value greater than 0 so we extend an arrow to the right.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"B <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Practice-Problems-4-b.png\\\"\/>\",\n                                \n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The number is greater than 0. x > 0 so, 0 is the limit value and it is not the solution of given inequality hence an open circle. The variable can take any value greater than 0 so we extend an arrow to the right.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"D <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Practice-Problems-4-d.png\\\"\/>\",\n                                \n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The number is greater than 0. x > 0 so, 0 is the limit value and it is not the solution of given inequality hence an open circle. The variable can take any value greater than 0 so we extend an arrow to the right.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"C\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The number is greater than 0. x > 0 so, 0 is the limit value and it is not the solution of given inequality hence an open circle. The variable can take any value greater than 0 so we extend an arrow to the right. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Practice-Problems-4-c.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The number is greater than 0. x > 0 so, 0 is the limit value and it is not the solution of given inequality hence an open circle. The variable can take any value greater than 0 so we extend an arrow to the right. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Practice-Problems-4-c.png\\\"\/>\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"5-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-79fa992e-b2fb-4184-97de-97e43e8d59bc\" 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-0-79fa992e-b2fb-4184-97de-97e43e8d59bc\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-79fa992e-b2fb-4184-97de-97e43e8d59bc\"><strong>Can we add and subtract in the inequality?<\/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-0-79fa992e-b2fb-4184-97de-97e43e8d59bc\">\n\n<p>Inequalities are very much like equations. If you want to add or subtract from one side of the equation, you must perform the same operation to the other side of the equation.&nbsp;<\/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-1-79fa992e-b2fb-4184-97de-97e43e8d59bc\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-79fa992e-b2fb-4184-97de-97e43e8d59bc\"><strong>Does inequality sign remain the same always?\u00a0<\/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-1-79fa992e-b2fb-4184-97de-97e43e8d59bc\">\n\n<p>No, the inequality sign is reversed when we multiply or divide each side with a negative number. The sign is also reversed when we exchange the values (If <em>p<\/em> &gt; <em>q<\/em>, then <em>q<\/em> &lt; <em>p)<\/em>&nbsp;or take reciprocal (If <em>p<\/em> &gt; <em>q<\/em>, then $\\frac{1}{p}$ &lt; $\\frac{1}{q}$).<\/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-2-79fa992e-b2fb-4184-97de-97e43e8d59bc\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-79fa992e-b2fb-4184-97de-97e43e8d59bc\"><strong>How many solutions does an inequality have?<\/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-2-79fa992e-b2fb-4184-97de-97e43e8d59bc\">\n\n<p>&nbsp;Inequalities have infinite solutions. for example x &lt; 5 will have all numbers less than 5 as solutions.<\/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-3-79fa992e-b2fb-4184-97de-97e43e8d59bc\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-79fa992e-b2fb-4184-97de-97e43e8d59bc\"><strong>How are inequalities different from 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-3-79fa992e-b2fb-4184-97de-97e43e8d59bc\">\n\n<p>Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality we compare the relative size of values, the two expressions are not necessarily equal which is indicated by the symbols: &gt;, &lt;, \u2264 or \u2265.<\/p>\n\n<\/div><\/div>\n<\/div>\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"6-lets-do-it\">Let&#8217;s do it!<\/h3>\n\n\n\n<p class=\" eplus-wrapper\">Learning inequality in math is important as it is a fundamental concept that takes a larger shape in higher classes. To make more mathematical concepts easier and fun for your kids, head over to <a href=\"https:\/\/www.splashlearn.com\/\">SplashLearn<\/a> and sign up for free!<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>In mathematics, a relationship between two expressions or values that are not equal to each other is called \u2018inequality.\u2019 So, a lack of balance results in inequality. For example, if you want to buy a new bicycle that costs $250, but you have $225. It is also an inequality as you are comparing two numbers &#8230; <a title=\"Inequality &#8211; Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/counting-and-comparison\/inequality\" aria-label=\"More on Inequality &#8211; Definition with Examples\">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-1165","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\/1165","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=1165"}],"version-history":[{"count":9,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1165\/revisions"}],"predecessor-version":[{"id":24460,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1165\/revisions\/24460"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1165"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1165"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1165"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}