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Solve the equation |x| - x = 0 for real x.
- x >= 0 (all non-negative reals)
- x <= 0 (all non-positive reals)
- x = 0 only
- all real x
Correct answer: x >= 0 (all non-negative reals)
Solution
|x| - x = 0 means |x| = x. By definition |x| = x exactly when x is non-negative; for x < 0, |x| = -x != x. Therefore the solution set is all x >= 0.
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