Given, x ∈ {integers}, find the solution set of : -5 ≤ 2x - 3 < x + 2.

Given,

-5 ≤ 2x - 3 < x + 2

Solving L.H.S. of the equation,

⇒ -5 ≤ 2x - 3

⇒ 2x ≥ -5 + 3

⇒ 2x ≥ -2

⇒ x ≥ -1 ………(i)

Solving R.H.S. of the equation,

⇒ 2x - 3 < x + 2

⇒ 2x - x < 2 + 3

⇒ x < 5 ………(ii)

From (i) and (ii) we get,

-1 ≤ x < 5

∴ Solution set = {-1, 0, 1, 2, 3, 4}.