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

$\dfrac{3}{5} \times x - \dfrac{2x - 1}{3} \gt 1 , x ∈ I$

$\Rightarrow \dfrac{3x}{5} - \dfrac{2x-1}{3} \gt 1$

Multiplying by 15 on both sides we get,

$\Rightarrow 15\Big(\dfrac{3x}{5} - \dfrac{2x-1}{3} \Big)\gt 15(1)$

⇒ 9x - 5(2x - 1) > 15

⇒ 9x - 10x + 5 > 15

⇒ -x + 5 > 15

⇒ x < 5 - 15

⇒ x < -10.

Since, x ∈ I.

Hence, solution set = {-11, -12, -13,…}.

Solution on the number line is :