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.