Check a Solution

Pronunciation: /tʃɛk eɪ səˈlu ʃən/ ?

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 to the equation 0=x^2-5x+6?

StepEquationDescription
1x=3, 0=x^2-5x+6These are the criteria.
20=3^2-5*3+6Use the substitution property of equality
30=9-15+6Simplify each term of the equation.
40=-6+6Simplify 9-15 = -6.
50=0Simplify the equation. Since the statement 0=0 is always true, x=3 is a solution to 0=x^2-5x+6.
Table 1: Example 1

Example 1

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

StepEquationDescription
1x=-2, 0=x^2-2x-3These are the criteria.
20=(-2)^2-2*(-2)-3Use the substitution property of equality
30=4-(-4)-3Simplify each term of the equation.
50=5Simplify the equation. Since the statement 0=5 is never true, x=-2 is never a solution to 0=x^2-2x-3.
Table 2: Example 2

Cite this article as:


Check a Solution. 2008-11-25. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/checkasolution.html.

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2008-11-25: Initial version (McAdams, David.)

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