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 a solution of the equation ?
Step | Equation | Description | |
---|---|---|---|
1 | , | These are the criteria. | |
2 | Use the substitution property of equality | ||
3 | Simplify each term of the equation. | ||
4 | Simplify 9-15 = -6. | ||
5 | Simplify the equation. Since the statement is always true, is a solution to . | ||
Table 1: Example 1 |
Is a solution to the equation ?
Step | Equation | Description | |
---|---|---|---|
1 | , | These are the criteria. | |
2 | Use the substitution property of equality | ||
3 | Simplify each term of the equation. | ||
4 | Simplify the equation. Since the statement is never true, is never a solution to . | ||
Table 2: Example 2 |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | Y |
Z | X |
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