Mathematics

Amos

21 October, 11:02

Analyze the solution shown.

1. - |-x| = 7: given

2. |-x| = - 7: multiplication property of equality

3. - x = 7 or - x = - 7: definition of absolute value

4. x = - 7 or x = 7: multiplication property of equality

5. Check: - | - (-7) | = 7, - 7 ≠ 7

-|-7| = 7, 7 = 7

Negative times negative is positive.

Determine the flaws in the solution.

The multiplication property of equality in Step 2 should result in |x| = 7.

The definition of absolute value is applied incorrectly. There is no solution.

The reason in Step 4 should be the addition property of equality.

The multiplication property of equality in Step 4 should result in only x = 7.

In evaluating the solutions, the absolute value should be simplified first to get a positive value.