Verified answer

|3x + 5| - |x - 4| ≤ 1

3x + 5 = 0   ⇒   x = - 1 2/3             x - 4 = 0   x = 4

1) x < - 1 2/3

- (3x + 5) + (x - 4) ≤ 1

- 3x - 5 + x - 4 ≤ 1

- 2x - 9 ≤ 1

-2x ≤ 10

x ≥ - 5

x ∈ [- 5 ; - 1 2/3)

2) - 1 2/3 ≤ x < 4

3x + 5 + x - 4 ≤ 1

4x + 1 ≤ 1

4x ≤ 0

x ≤ 0

x ∈ [- 1 2/3 ; 0]

3) x ≥ 4

3x + 5 - x + 4 ≤ 1

2x + 9 ≤ 1

2x ≤ - 8

x ≤ - 4 - неуд

Ответ : x ∈ [- 5 ; 0]