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HomeUS High SchoolMathematicsAbsolute Value Equations and Inequalities › The equation absolute value of z equals 0 has ho…

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_
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