Question

Для каждого значения параметра b решите уравнение 3x-|bx-2|=0

Answer 1

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