Let |x| = y. Then

\(\frac{|x|-1}{|x|-2}\) ≥ 0 ⇒ \(\frac{y-1}{y-2}≥0\)

On equating (y – 1) and (y – 2) equal to zero, we have the critical points as y = 1, 2. Now using the real number line, we see that the expression \(\frac{y-1}{y-2}\) is greater than equal to zero (positive) only when, y __<__ 1 or y > 2.

⇒ |x| __<__ 1 or |x| > 2

⇒ –1 __<__ x __<__ 1 or (x < –2 or x > 2)

⇒ \(x\)∈ [–1, 1] ∪ (–∞, –2) ∪ (2, ∞)