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:
Is x = 3 a solution of the equation 0 = x2 - 5x + 6?
|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|
Is x = -2 a solution to the equation 0 = x2 - 2x - 3?
|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|
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