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**Solve: {|x| - 1}/{|x| - 2} ≥ 0 x ∈ R, x ≠ ± 2**

**Solution:** We have, {|x| - 1}/{|x| - 2} ≥ 0

=> (y - 1)/(y - 2) ≥ 0, where y = |x|

=> y ≤ 1 or y > 2

=> |x| ≤ 1 or |x| > 2

=> (-1 ≤ x ≤ 1) or (x < -2 or x > 2)

=> x ∈ [-1, 1] or x ∈ (-∞, -2) U (2, ∞)

=> x ∈ [-1, 1] U (-∞, -2) U (2, ∞)