Q. The set of all real $x$ satisfying the inequality $\frac{3 - |x|}{4 - |x|} > 0$
A) $\lbrack - 3,\ 3\rbrack \cup ( - \infty,\ - 4) \cup (4,\ \infty)$
B) $( - \infty,\ - 4) \cup (4,\ \infty)$
C) $( - \infty,\ - 3) \cup (4,\ \infty)$
D) $( - \infty,\ - 3) \cup (3,\ \infty)$
Explanation
(a)
Given, $\frac{3 - |x|}{4 - |x|} \geq 0$
$\Rightarrow \ \ 3 - |x| \leq 0$ and $4 - |x| < 0$
Or $3 - |x| \geq 0$ and $4 - |x| > 0$
$\Rightarrow \ \ |x| \geq 3$ and $|x| > 4$
Or $|x| \leq 3$ and $|x| < 4$
$\Rightarrow \ \ \ |x| > 4$ or $|x| \leq 3$
$\Rightarrow ( - \infty,\ - 4) \cup \lbrack - 3,\ 3\rbrack \cup (4,\ \infty)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.