If |z - 7| - 2 = 2, then z = - 3 / amp; z = - 11 true or false

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