Verified answer

|x| - |x - 2| = 2

1) x ∈ (- ∞ ; 0)

- x - (2 - x) = 2

- x - 2 + x = 2

0 * x = 4

x ∈ ∅

2) x ∈ [0 ; 2)

x - (2 - x) = 2

x - 2 + x = 2

2x = 4

x = 2 - неуд , так как 2 ∉ [0 ; 2)

3) x ∈ [2 ; + ∞)

x - (x - 2) = 2

x - x + 2 = 2

0 * x = 0

x ∈ [2 ; + ∞)

Ответ : x ∈ [2 ; + ∞)