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Find all real x satisfying |x| + |x + 1| + |x + 2| = 3.

1. x = 0 and x = -2
2. x = -1 only
3. x = 0 only
4. no real solution

Correct answer: x = 0 and x = -2

Solution

The piecewise-linear sum has its minimum value 2 at x = -1 and increases on either side; setting it to 3 gives the two boundary solutions.

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