Для каждого значения параметра b решите уравнение

3x-|bx-2|=0

3x = |bx-2|

=> x ≥ 0

1) bx - 2 = 3x, x ≥ 2/b (b≠0)

(b - 3) x = 2

x = 2 / (b-3), b≠3

2) 2 - bx = 3x, x < 2/b

(3+b) x = 2

x = 2 / (b+3), b≠ - 3

3) b = 0

3x - 2 = 0

x = 2/3

4) b = 3

3x = - 3x + 2

6x = 2

x = 2/6 < 2/3 - подходит

5) b = - 3

3x = - 3x - 2

6x = - 2

x = - 1/3 > - 2/3 - подходит

Ответ: b = 0 = > x = 2/3

b = - 3 = > x = - 1/3

b = 3 = > x = 1/3

x = 2 / (b-3), x ≥ 2/b, b ≠3

x = 2 / (b+3), x < 2/b, b≠-3