Question

|x + 2| + 16 = 14

x = −32 and x = −4

x = −4 and x = 0

x = 0 and x = 28

No solution

Answer 1

|x + 2| = 14 - 16 = -2
x + 2 = -2 and x + 2 = 2
x = -2 - 2 and x = 2 - 2
x = -4 and x = 0

To check for extraneous solutions:
For x = -4
|-4 + 2| + 16 = |-2| + 16 = 2 + 16 = 18 ≠ 14, hence solution is not valid

For x = 0
|0 + 2| + 16 = |2| + 16 = 2 + 16 = 18 ≠ 14, hence solution is not valid

Therefore the equation has no solution.