CAT 2024 Slot 2 QA Question 9: All the values of $x$ satisfying the inequality $\dfrac{1}{x+5} \leq \dfrac{1}{2x-3}$ are

Question

All the values of $x$ satisfying the inequality $\dfrac{1}{x+5} \leq \dfrac{1}{2x-3}$ are

Accepted Answer

Move all terms to one side.
$\dfrac{1}{x+5} - \dfrac{1}{2x-3} \leq 0$
$\Rightarrow \dfrac{(2x-3)-(x+5)}{(x+5)(2x-3)} \leq 0$
$\Rightarrow \dfrac{x-8}{(x+5)(2x-3)} \leq 0$
The critical values are $x = -5$, $x = \dfrac{3}{2}$ and $x = 8$. The expression is defined only when $x 
eq -5$ and $x 
eq \df

All the values of xxx satisfying the inequality 1x+5≤12x−3\dfrac{1}{x+5} \leq \dfrac{1}{2x-3}x+51​≤2x−31​ are

All the values of $x$ satisfying the inequality $\dfrac{1}{x+5} \leq \dfrac{1}{2x-3}$ are