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 = x^{2} - 5x + 6?
Step | Equation | Description | |
---|---|---|---|
1 | x = 3, 0 = x^{2} - 5x + 6 | These are the criteria. | |
2 | 0 = 3^{2} - 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 = x^{2} - 5x + 6. | |
Table 1: Example 1 |
Is x = ^{-}2 a solution to the equation 0 = x^{2} - 2x - 3?
Step | Equation | Description | |
---|---|---|---|
1 | x = ^{-}2, 0 = x^{2} - 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 = x^{2} - 2x - 3. | |
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 | X |
Y | Z |
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