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The property of equality that justifies the step from
\[
\frac{3z}{2} - 5 = 10
\]
to
\[
\frac{3z}{2} - 5 + 5 = 10 + 5
\]
is the **Addition Property of Equality**.
This property states that if you add the same number to both sides of an equation, the two sides remain equal. In this case, adding \(5\) to both sides of the equation is what justifies the step.