DETERMINING WHETHER VALUES ARE SOLUTIONS

An equation is a mathematical statement that two expressions are equal. An equation may or may not contain variables. For an equation that contains a variable, a solution of the equation is a value of the variable that makes the equation true.

Solved Examples

Example 1 : 

Determine whether the x = 6 is a solution of the equation x + 9  =  15.

Solution : 

Substitute x  =  6 in the given equation.

6 + 9  =  15 ?

Add 6 and 9.

15  =  15 ?

For the question 15 = 15 ?, we have to say the answer 'yes'. 

Because 15 is equal to 15 (Same values).

So, 6 is a solution to the equation x + 9  =  15. 

Example 2 : 

Determine whether the y = 8 is a solution of the equation y/4  =  32.

Solution : 

Substitute y  =  8 in the given equation.

8 / 4  =  32 ?

Divide 8 by 4.

2  =  32 ?

For the question 2 = 32 ?, we have to say the answer 'No'. 

Because 2 is not equal to 15 (Different values).

So, 8 is not a solution to the equation y/4  =  32. 

Example 3 : 

Determine whether the x = 9 is a solution of the equation 8x  =  72.

Solution : 

Substitute x  =  9 in the given equation.

8(9)  =  72 ?

Multiply 8 and 9.

72  =  72 ?

For the question 72 = 72 ?, we have to say the answer 'yes'. 

Because 72 is equal to 72 (Same values).

So, 9 is a solution to the equation 8x  =  72. 

Example 4 : 

Determine whether the n = 5 is a solution of the equation 11  =  n + 6.

Solution : 

Substitute n  =  5 in the given equation.

11  =  5 + 6 ?

Add 5 and 6.

11  =  11 ?

For the question 11 = 11 ?, we have to say the answer 'yes'. 

Because 11 is equal to 11 (Same values).

So, n = 5 is a solution of the equation 11  =  n + 6. 

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