Question

Which property of equality justifies the step for solving the equation that is displayed? 3z/2 -5=10

Answer 1

To solve the equation \( \frac{3z}{2} - 5 = 10 \), the first step typically involves isolating the term containing the variable.

1. To eliminate the constant on the left side, you would add \( 5 \) to both sides of the equation. This step uses the **Addition Property of Equality**, which states that if you add the same number to both sides of an equation, the two sides remain equal.

So, from \( \frac{3z}{2} - 5 = 10 \), adding \( 5 \) gives:

\[
\frac{3z}{2} - 5 + 5 = 10 + 5
\]

This simplifies to:

\[
\frac{3z}{2} = 15
\]

This justifies the use of the Addition Property of Equality in this step of solving the equation.