Find the values of x, which satisfy the inequation:

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

Graph the solution set on the number line.

Given,

$-2 \le \dfrac{1}{2} - \dfrac{2x}{3} \le 1\dfrac{5}{6} \\[0.5em] \Rightarrow -2 \le \dfrac{1}{2}-\dfrac{2x}{3} \le \dfrac{11}{6} \\[0.5em] \Rightarrow -2-\dfrac{1}{2} \le \dfrac{1}{2} - \dfrac{2x}{3} - \dfrac{1}{2} \le \dfrac{11}{6} - \dfrac{1}{2}\\[0.5em] \text {By subtracting } \dfrac{1}{2} \text{ on both sides of inequality in the above line.}\\[0.5em] \Rightarrow -\dfrac{5}{2} \le -\dfrac{2x}{3} \le \dfrac{8}{6} \\[0.5em] \Rightarrow -\dfrac{5}{2} \times 6 \le -\dfrac{2x}{3}\times 6 \le \dfrac{8}{6}\times 6 \text{ (Multiplying complete equation with 6) } \\[0.5em] \Rightarrow -15 \le -4x \le 8 \\[0.5em] \Rightarrow 15 \ge 4x \ge -8 \\[0.5em] \Rightarrow \dfrac{15}{4} \ge x \ge -2$

Since x ∈ N,

∴ Solution Set = {1, 2, 3}

The graph of the solution set is shown by thick dots on the number line.