Solve the following inequation and represent the solution set on a number line.

$-8\dfrac{1}{2} \lt -\dfrac{1}{2} - 4x \le 7\dfrac{1}{2}$, x ∈ I

Given,

$-\dfrac{17}{2} \lt -\dfrac{1}{2} - 4x \le \dfrac{15}{2}$

Solving L.H.S. of the inequation,

$\Rightarrow -\dfrac{17}{2} \lt -\dfrac{1}{2} - 4x \\[1em] \Rightarrow 4x \lt -\dfrac{1}{2} + \dfrac{17}{2} \\[1em] \Rightarrow 4x \lt \dfrac{16}{2} \\[1em] \Rightarrow 4x \lt 8 \\[1em] \Rightarrow x \lt 2 ……(i)$

Solving R.H.S. of the inequation,

$\Rightarrow -\dfrac{1}{2} - 4x \le 7\dfrac{1}{2} \\[1em] \Rightarrow \dfrac{-1 - 8x}{2} \le \dfrac{15}{2} \\[1em] \Rightarrow -8x \le 15 + 1 \\[1em] \Rightarrow 8x \ge -16 \\[1em] \Rightarrow x \ge -2 …….(ii)$

From (i) and (ii) we get,

-2 ≤ x < 2

Since, x ∈ I

∴ Solution set = {-2, -1, 0, 1}.

Solution on the number line is :