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Determine the collection of real numbers x for which both |x − 1| ≤ 3 and |x − 1| ≥ 1 hold simultaneously.

1. [2, 4]
2. (−∞, 2] ∪ [4, +∞)
3. [−2, 0] ∪ [2, 4]
4. None of these

Correct answer: [−2, 0] ∪ [2, 4]

Solution

|x-1|<=3 gives -2<=x<=4. |x-1|>=1 gives x<=0 or x>=2. Intersection is [-2,0] U [2,4].

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