Question

The solution set of the inequation $\frac{3}{|x|+2}\ge 1$ is

• A. $[-1,1]$
• B. $(-1,1)$
• C. $(-\infty ,1]$
• D. $[1,\infty )$

Answer 1

The correct option is A $[-1,1]$

$\frac{3}{|x|+2}\ge 1$
$\Rightarrow 3\ge |x|+2(\because |x|+2>0\forall x\in R)$
$\Rightarrow |x|\le 1$
$\Rightarrow -1\le x\le 1$