The solution set of the inequation $|[|x|-7]| -5<0$ is ([.] denotes the greatest integer function)
Answer & explanation
Correct answer: option 4
We have,
$|[|x|-7]| -5<0$
$⇒|[|x|-7]| <5$
$⇒-5<[|x|-7] <5$
$⇒-4≤|x|-7 <5$
$⇒3≤|x|<12 ⇒ x ∈(−12, – 3] ∪[3,12)$