Answer:
False
Step-by-step explanation:
The absolute value always returns a positive value, however the expression inside can be positive or negative, that is
Given
| z - 7 | - 2 = 2 ( add 2 to both sides )
| z - 7 | = 4, then
z - 7 = 4 OR - (z - 7) = 4
z = 4 + 7 = 11 OR
- z + 7 = 4
- z = 4 - 7 = - 3 ( multiply both sides by - 1 )
z = 3
As a check
z = 11
| 11 - 7 | - 2 = | 4 | - 2 = 4 - 2 = 2 ← True
z = 3
| 3 - 7 | - 2 = | - 4 | - 2 = 4 - 2 = 2 ← True
Hence z = 11 or z = 3 are the solutions
