2x/3 - (x - 1)/6 + (x + 2)/2 ≥ 0

4x/6 - (x - 1)/6 + 3*(x + 2)/6 ≥ 0

(4x - (x - 1) + 3*(x + 2))/6 ≥ 0

(4x - x + 1 + 3x + 6)/6 ≥ 0

(6x + 7)/6 ≥ 0

6x + 7 ≥ 0

6x ≥ -7

x ≥ -7/6

x ≥ -1 1/6

x ∈ [-1 1/6; +∞)