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Solve for real x: |x| - 2|x + 1| + 3|x + 2| = 0.

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

Correct answer: x = -2 only

Solution

An absolute-value equation is solved piecewise across the points where each modulus changes sign; a candidate root counts only if it falls within the interval used to derive it.

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