Question

The set of all real x satisfying the inequality $\frac{3-|x|}{4 - |x|} \ge 0 $ , is

• A. $[-3,3] \cup(-\infty,-4) \cup(4, \infty)$
• B. $(-\infty,-4) \cup(4, \infty)$
• C. $(-\infty,-3) \cup(4, \infty)$
• D. $(-\infty,-3) \cup(3, \infty)$

Answer 1

Answer: (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 $|x| \leq 3$
$\Rightarrow x \in(-\infty,-4) \cup[-3,3] \cup(4, \infty)$