Find the value of x which satisfies the inequation :

-2 ≤ $\dfrac{1}{2} - \dfrac{2x}{3} \le 1\dfrac{5}{6}$, x ∈ W.

Also, graph the solution on a number line.

Solving L.H.S. of the above inequation :

$\Rightarrow -2 \le \dfrac{1}{2} - \dfrac{2x}{3} \\[1em] \Rightarrow \dfrac{2x}{3} \le \dfrac{1}{2} + 2 \\[1em] \Rightarrow \dfrac{2x}{3} \le \dfrac{5}{2} \\[1em] \Rightarrow x \le \dfrac{5}{2} \times \dfrac{3}{2} \\[1em] \Rightarrow x \le \dfrac{15}{4} \text{ ………(1) }$

Solving R.H.S. of the above inequation :

$\Rightarrow \dfrac{1}{2} - \dfrac{2x}{3} \le 1\dfrac{5}{6} \\[1em] \Rightarrow \dfrac{1}{2} - \dfrac{2x}{3} \le \dfrac{11}{6} \\[1em] \Rightarrow \dfrac{2x}{3} \ge \dfrac{1}{2} - \dfrac{11}{6}\\[1em] \Rightarrow \dfrac{2x}{3} \ge \dfrac{3 - 11}{6} \\[1em] \Rightarrow x \ge -\dfrac{8}{6} \times \dfrac{3}{2} \\[1em] \Rightarrow x \ge -2 \text{ …….(2)}$

From (1) and (2), we get :

-2 ≤ x ≤ $\dfrac{15}{4}$

Since, x ∈ W.

x = {0, 1, 2, 3}

Hence, x = {0, 1, 2, 3}.