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The equation absolute value of z equals 0 has how many solutions?
AExactly two
BNone at all
CInfinitely many
DExactly one
Answer & Solution
Correct answer: D. Exactly one
1. The two equivalent equations are z equal to 0 and z equal to negative 0.
2. Negative 0 and 0 are the same number.
3. So both branches collapse onto the single value 0.
4. A positive right side would split into two distinct answers, but 0 does not.
_Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.7 Solve Absolute Value Inequalities_