Given x ∈ {real numbers}, find the range of values of x for which -5 ≤ 2x - 3 < x + 2 and represent it on a real number line.

Given,

-5 ≤ 2x - 3 < x + 2

Solving L.H.S. of the equation,

⇒ -5 ≤ 2x - 3

⇒ 2x ≥ -5 + 3

⇒ 2x ≥ -2

Dividing both sides by 2 we get,

⇒ 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 = {x : x ∈ R and -1 ≤ x < 5}.

Solution on the number line is :