Solve: $\frac{-1}{|x|-2}≥1$
Answer & explanation
Correct answer: option 4
Given $\frac{-1}{|x|-2}≥1$
$⇒\frac{-1}{|x|-2}-1≥0$
$⇒\frac{-1(|x|-2)}{|x|-2}≥0$
$⇒\frac{1-|x|}{|x|-2}≥0$
$⇒\frac{|x|-1}{|x|-2}≤0$
$⇒\frac{y-1}{y-2}≤0$, where $y = |x|$
$⇒1≤y<2$
$⇒1≤|x|<2$
$⇒x∈(-2,-1]∪[1,2)$