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, $\frac{3-|x|}{4-|x|}\ge 0$
$\Rightarrow 3-|x|\le 0$ and $4-|x|<0$
or $3-|x|\ge 0$ and $4-|x|<0$
$\Rightarrow |x|\ge 3$ and $|x|>4$
or $|x|\le 3$ and $|x|<4$
$\Rightarrow |x|>4$ or $|x|\le 3$
$\Rightarrow x\in (-\infty ,-4)\cup [-3,3]\cup (4,\infty )$