Difference Between Constants and Variables for JEE Main 2024

When we learn the term equation we have to first understand the terms of constant and variable. These terms are used at every step in Algebra. We must be quite familiar with what is the difference between constant and variable. 

Let us consider a real-life example:

The height of a kid and the dress of a kid. Here the height of a kid is variable because it will keep on changing over the period of time but the dress of a kid will remain the same forever so it is a constant.

So let us see the definition of constant and variable.

Definition of Constant: 

As the name implies, the constant is a value that remains constant ever. Constant has a fixed value and its value cannot be changed by any variable. Constants are represented by numbers.

For example in the algebraic expression 

3x + 5y = 7, where 7 is the constant we know its face value is 7 and it cannot be changed. But 3x and 5y are not constants because the variable x and y can change their value.

Definition of Variable: 

A value that keeps on changing is said to be variable. Variables are often represented by an alphabet like a, b, c, or x, y, z. Its value changes from time to time.

For example in the Algebraic Expression:

3x + 5y = 7 where x and y are variables that are changed according to the expression.

Below is the tabular format of the difference between variable and constant. It will make you more clear what is variable and constant.

Difference between Constant and Variables

From the above table now you have a clear picture of what is the difference between constant and variable. 

Now let us solve some examples which will make it more clear what is variable and constant.

Solved Examples

Example 1 : 

Find the value of x for the equation x - 4  =  0

Solution :

x - 4  =  0

Add 4 to each side. 

X - 4 + 4 = 4

x  =  4

So, the value of x is 4. 

Example 2 : 

Find the value of x for the equation 3x  =  27

Solution : 

3x  =  27

Divide each side by 3.

3x/3  =  27/3

x = 9

So, the value of x is 9

Example 3 : 

Find the value of x  for the equation x + 5  =  -2

Solution :

x + 5 =  -2

Subtract 5 from each side. 

x + 5 - 5 = -2 -5

x  =  -7

So, the value of x is -7.

Example 4 : 

Find the value of x for equation 4x + 6  =  22.

Solution :

4x + 6  =  22

Subtract 6 from each side.

4x + 6 - 6  =  22 - 6

4x = 16

Divide each side by 4.

4x/4  =  16/4

x = 4

So, the value of x is 4

So from these problems, we have got different values for the same alphabet x.the values of x keeps on changing depending upon the equation,

So alphabet x is said to be variable. 

Quiz Time

Find the value of x for the following equation

1. 5x + 10 = 15

2. 7x + 7 = 28

3. x + 15 = 20

4. x - 8 = 2

Points to remember with the Difference between Constants and Variables

Constants and Variables are one the easiest and most fundamental concepts of Mathematics. In fact, Constants and Variables form the mathematical equations and thus should be learned before solving the mathematical equations. Vedantu has explained the difference between Constants and Variables in a very easy-to-understand manner where students can use the concepts to easily differentiate Constants and Variables from one another. Given below are some of the basic and important points regarding Constants and Variables. 

• Constants are values that will not change under any circumstances. That means that the values of constants are fixed and will not vary in any condition given in the question. Hence, we can easily determine the constant in an equation. We need to simply choose the value which will not change even though conditions change for the given equation or the question. Constants can be whole numbers, they can also be fractions or decimal numbers or rational or irrational numbers as well. As these numbers are fixed, they will not change under any condition and hence they are called the constant in the equations. If any question is asked to determine the constant in the equation, one should look for the numbers stated in the previous question. This will ensure a correct answer and full marks in such questions.

• Variables the symbols will undergo change if there is a change in the condition as stated in the question or equation given. Variables are easy to understand and identify as they are often represented by alphabetical symbols such as x, y, z, a, m0, m1, k, w, q, p1, p2, p3, and many more. As the name Variable says, they vary under different conditions. Thus, variables can hold multiple values which can satisfy the equation. They can also hold no value in some cases in which we conclude that the equation holds no solution. Variables can also hold infinite values. In such scenarios, we call this as the equation holds infinitely many solutions. The variables can also hold a specific set of numbers.

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