Question

How to solve for x, if |x-1| ≥ 3?

(a) (-∞, -2) ∪ (4, ∞)

(b) (-∞, -2] ∪ [4, ∞)

(c) (0, -2] ∪ (4, 0)

(d) (-∞, ∞) – {-2, 4}

The question was posed to me during a job interview.

The question is from Sets and their Representations in division Sets of Mathematics – Class 11

Answer 1

Right choice is (b) (-∞, -2] ∪ [4, ∞)

Easy explanation: Given, |x-1| ≥ 3

= x-1 < -3 or x – 1 ≥ 3

= x ≤ -2 or x ≥ 4

Hence, x c (-∞, -2] ∪ [4, ∞).