Q46 / 125 · BITSAT 2013 · Mathematics

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

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

Solution

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

Hence, the correct answer is option: 'A'.

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