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For real x, the solution set of the inequality |x - |x - 1| - 1| ≤ 1 is

1. [-1, 3]
2. [0, 2]
3. [-1, 1]
4. None of these

Correct answer: None of these

Solution

For x>=1, x-|x-1|-1 = x-(x-1)-1 = 0, so |0|<=1 holds for all x>=1. For x<1, the expression is |2x-2|<=1 giving 1/2<=x<1. Combining, the solution set is [1/2, infinity), which is none of the listed finite intervals.

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