Variable in Math – Definition with Examples

What is Variables?

In real-life there are things that remain constant like your date of birth. However, there are things that vary with time and place like temperature, age, height etc. Since these quantities change they are may be called variables. 

In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation or an algebraic expression. In simple words, a variable is a quantity that can be changed and is not fixed. Variables are essential as they form a major algebra component.

We usually use “x” and “y” to express an unknown integer. However, it isn’t necessary, and we can use any letter.

Explanation of Variable

Example- 
Let us take an example of the algebraic expression 2x + 6. Here, x is a variable and can take any value. If x = 1, the value of this algebraic expression will be 2(1) + 6 i.e. 8 and 

if x = 2, the value of the algebraic expression changes to 10. Hence, we can say that the value of the algebraic expression varies as the x varies. 

Now let us consider an equation 2x + 6 = 12.  

The variable x can take any value in an equation also. It may or may not satisfy the equation. If it does, it is called the solution of the equation.

Value of x LHS
2x + 6 
RHS
12
1 2(1) + 6 = 812
2 2(2) + 6 = 1012
3 2(3) + 6 = 1212

Here, x = 3 makes the equation true and is called the solution of this equation.

Different Types of Variables

There are two types of variables: Dependent Variables and Independent variables.

Different Types of Variable


Dependent Variables

The dependent variable is a variable whose value is determined by the quantity another variable takes. 

For instance, in the equation y = 2x + 3, x can take any value, like 1, 2, 3. However, the value of y will depend on the value of x. So, if x = 1, y will become 5, and if x = 2, y will become 7, and so on. Therefore, y is called the dependent variable and x is called the independent variable.

Independent Variable, xDependent Variable, y = 2x + 3
03
15
27

Independent Variables

An independent variable in an algebraic equation is one whose values are unaffected by changes. If an algebraic equation has two variables, x, and y, and each value of x is related to any other value of y, then x is an independent variable, and y is a dependent variable.

For instance, in the equation y = 2x, x can take any value. Hence, it is the independent variable in the equation.

Conclusion

Variables are a very important concept if you want to understand algebra. At SplashLearn, you will come across various resources, like games and worksheets, that will help you understand the concept of variables. The solved examples and practice problems give a step-by-step understanding, making it easier to solve sums on your own. 

Solved Examples:

  1. Find one value of x that satisfies the equation 6x + 4 = 22 and one value that does not.

Solution:

Value of x LHS RHS
06(0) + 4 = 422LHS $\neq$ RHS
36(3) + 4 = 2222LHS = RHS

x = 0  does not satisfy the equation as LHS is not equal to RHS.

x = 3 satisfy the equation as LHS is equal to RHS. So, x = 3 is the solution for the given equation.

  1. Is h = 3, the solution of equation 7h − 2 = 12?

Solution:

7(3) − 2 = 21 − 2 = 19

19 $\neq$ 12

So, h = 3 is not a solution of a given equation.

  1. What will be the value of the expression 3x + 2 when x = 4?

Solution:

3(4) + 2 = 12 + 2 = 14

Practice Problems

Variable

Attend this Quiz & Test your knowledge.

1The value of a in the equation a + 62 = 39 is

2
3
4
5
CorrectIncorrect
Correct answer is: 3
3 + 62 = 3 + 36 = 39

2Consider the equation x + y = 20. If the value of x is 14, the value of y will be

2
5
6
10
CorrectIncorrect
Correct answer is: 6
14 + 6 = 20

3Which of the following equation has y = 3 as a solution?

y - 4 = 1
y + 3 = 0
2y - 5 = 2
y - 3 = 0
CorrectIncorrect
Correct answer is: y - 3 = 0
3 - 3 = 0

4A variables

can take only 1 value
can take only 2 values
has a fixed value
can take different values
CorrectIncorrect
Correct answer is: can take different values
A variable can take any value and hence do not have any fixed value.

Frequently Asked Questions

Variables are used to represent the unknown quantity.

Yes, we can use α (alpha), 𝛽 (beta), 𝛾 (gamma), 𝛳 (theta) and other letters also as a variable.

Yes, variables can take any value.

A combination of symbols, variables, and constants is called a variable expression. For example: 5x – 42