Question

When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step?
Original Equation:
Original Equation:
one fifth, x, equals, 5
5
1
​
x=
5
First Step:
First Step:
x, equals, 25
x=
25
Answer
Multiple Choice Answers
commutative property of multiplication
addition property of equality
commutative property of addition
multiplication property of equality

Answer 1

To determine which property justifies Carmen's first step in the equation \(\frac{1}{5}x = 5\) to \(x = 25\), let's analyze what happened.

Carmen multiplied both sides of the equation by 5 to eliminate the fraction:

\[
5 \left(\frac{1}{5}x\right) = 5 \cdot 5
\]

This simplifies to:

\[
x = 25
\]

The property that allows you to multiply both sides of an equation by the same number (in this case, 5) to maintain equality is the **multiplication property of equality**.

Therefore, the answer is:

**multiplication property of equality**.