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.