Short Answer Questions 2 — Question 4

Given,

$\dfrac{11 + 3x}{5} \ge 3 - x \gt -\dfrac{3}{2}$

Solving L.H.S. of the equation,

$\Rightarrow \dfrac{11 + 3x}{5} \ge 3 - x \\[1em] \Rightarrow 11 + 3x \ge 5(3 - x) \\[1em] \Rightarrow 11 + 3x \ge 15 - 5x \\[1em] \Rightarrow 3x + 5x \ge 15 - 11 \\[1em] \Rightarrow 8x \ge 4 \\[1em] \Rightarrow x \ge \dfrac{4}{8} \\[1em] \Rightarrow x \ge \dfrac{1}{2} \text{ ...........(1)}$

Solving R.H.S. of the equation,

$\Rightarrow 3 - x \gt -\dfrac{3}{2} \\[1em] \Rightarrow x \lt 3 + \dfrac{3}{2} \\[1em] \Rightarrow x \lt \dfrac{6 + 3}{2} \\[1em] \Rightarrow x \lt \dfrac{9}{2} \text{ .......(2)}$

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

$\Rightarrow \dfrac{1}{2} \le x \lt \dfrac{9}{2}$

Hence, solution set = {$x : \dfrac{1}{2} \le x \lt \dfrac{9}{2}, x ∈ R$}