Solve : |x|-1/|x|-2 >= 0

We have, \frac{|x| - 1}{|x| - 2} \geq 0 \Rightarrow \frac{y - 1}{y - 2} \geq 0 [Where y = |x|] \Rightarrow y \leq 1 or y > 2 \Rightarrow |x| \leq 1 or |x| > 2 \Rightarrow (- 1 \leq x \leq 1) or (x < - 2 or x > 2) \Rightarrow x \in [- 1, 1] or x \in (- \infty, - 2) \cup (2, \infty) \Rightarrow x \in [- 1, 1] \cup (- \infty, - 2) \cup (2, \infty) So, the solution set of the given inequation is [- 1, 1] \cup (- \infty, - 2) \cup (2, \infty) .