Solve the inequation given below and represent its solution set on a number line:

$\dfrac{(5x - 8)}{3} \ge \dfrac{(4x - 7)}{2}$, x ∈ R

Given,

⇒ $\dfrac{(5x - 8)}{3} \ge \dfrac{(4x - 7)}{2}$

Multiplying by 6 on both sides we get,

⇒ $6\Big(\dfrac{5x - 8}{3}\Big) \ge 6\Big(\dfrac{4x - 7}{2}\Big)$

⇒ 2(5x - 8) ≥ 3(4x - 7)

⇒ 10x - 16 ≥ 12x - 21

⇒ 10x - 12x ≥ -21 + 16

⇒ -2x ≥ -5

Dividing by -2 on both sides we get,

⇒ x ≤ $\dfrac{5}{2}$ (As on dividing by negative number the sign reverses.)

Since, x ∈ R

Hence, solution set = {x : x ≤ $\dfrac{5}{2}$, x ∈ R}.

Solution on the number line is :