Question

The set of all real $x$ satisfying the in equal $\frac{3-|x|}{4-|x|}\ge 0$

• 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)

$[-3,3]\cup (-\infty ,-4)\cup (4,\infty )$

Answer 2

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