Question

The solution set of the inequality $|[|x|-5]|-7<0$ is
$\left(\right[.]$ denotes the greatest integer function$)$

• A. $[-13,13]$
• B. $(-13,13)$
• C. $(-13,13)-\left\{5\right\}$
• D. $(-13,13)-\{\pm 5\}$

Answer 1

The correct option is B $(-13,13)$

$|[|x|-5]|-7<0$
$\Rightarrow |[|x|-5]|<7$
$\Rightarrow -7\le [|x|-5]\le 7\Rightarrow -7\le |x|-5<8\Rightarrow -2\le |x|<13\Rightarrow 0\le |x|<13\Rightarrow |x|<13\Rightarrow x\in (-13,13)$