# Check a Solution

Pronunciation: /tʃɛk eɪ səˈlu.ʃən/ Explain

To check a solution is to substitute a solution back into the original equation or inequality to see if it is a valid solution. The most common use of checking a solution is to verify that the math used to come up with the solution is correct. In addition, sometimes two solutions will be produced for a problem, but only one will be valid. To find out which of the solutions is valid, they are substituted back into the original equation.

There are three steps to checking a solution:

1. Substitute the solution into the original equation or inequality.
2. Simplify the equation or inequality.
3. Verify that the simplified equation or inequality is still true.

### Example 1

Is x = 3 a solution of the equation 0 = x2 - 5x + 6?

StepEquationDescription
1 x = 3, 0 = x2 - 5x + 6 These are the criteria.
2 0 = 32 - 5·3 + 6 Use the substitution property of equality
3 0 = 9 - 15 + 6 Simplify each term of the equation.
4 0 = -6 + 6 Simplify 9 - 15 = -6.
5 0 = 0 Simplify the equation. Since the statement 0 = 0 is always true, x = 3 is a solution to 0 = x2 - 5x + 6.
Table 1: Example 1

### Example 2

Is x = -2 a solution to the equation 0 = x2 - 2x - 3?

StepEquationDescription
1 x = -2, 0 = x2 - 2x - 3 These are the criteria.
2 0 = (-2)2 - 2·(-2) - 3 Use the substitution property of equality.
3 0 = 4 - (-4) - 3 Simplify each term of the equation.
4 0 = 5 Simplify the equation. Since the statement 0 = 5 is never true, x = -2 is never a solution to 0 = x2 - 2x - 3.
Table 2: Example 2
1. McAdams, David E.. All Math Words Dictionary, check a solution. 2nd Classroom edition 20150108-4799968. pg 33. Life is a Story Problem LLC. January 8, 2015. Buy the book