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

$2x + \dfrac{7}{2} \gt \dfrac{5x}{3} + 3, x ∈ I$

Given,

$\Rightarrow 2x + \dfrac{7}{2} \gt \dfrac{5x}{3} + 3$

Multiplying by 6 on both sides we get,

$\Rightarrow 6 \Big(2x + \dfrac{7}{2}\Big) \gt 6\Big(\dfrac{5x}{3}+3\Big)$

⇒ 12x + 21 > 10x + 18

⇒ 12x - 10x > 18 - 21

⇒ 2x > -3

⇒ x > $-\dfrac{3}{2}$

⇒ x > -1.5

Since, x ∈ I

Hence, solution set = {-1, 0, 1, 2, 3,….}.

Solution on the number line is :