Рассматриваем два случая:
1. 2x + 3 >= 0
x >= -1.5
|2x + 3 - 2| = 5
x >= -1.5
|2x +1| = 5
x >= -1.5
2x + 1 = 5
2x + 1 = -5
x >= -1.5
x = 2
x = -3
x = 2
2. 2x + 3 < 0
x < -1.5
|-2x - 3 - 2| = 5
x < -1.5
|-2x - 5| = 5
x < -1.5
-2x - 5 = 5
-2x - 5 = -5
x < -1.5
x = -5
x = 0
x = -5
Ответ: x = -5, x = 2