Question

When solving an equation, Emily's first step is shown below. Which property justifies Emily's first step?
Original Equation:
Original Equation:
one fifth, x, equals, minus, 2
5
1
​
x=
−2
First Step:
First Step:
x, equals, minus, 10
x=
−10

Answer 1

Emily's first step can be justified using the **Multiplicative Property of Equality**. This property states that if you multiply both sides of an equation by the same nonzero number, the two sides remain equal.

In the original equation:

\[
\frac{1}{5} x = -2
\]

Emily multiplied both sides by 5 to eliminate the fraction:

\[
5 \cdot \frac{1}{5} x = 5 \cdot (-2)
\]

This simplifies to:

\[
x = -10
\]

Therefore, the justification for Emily's first step is the **Multiplicative Property of Equality**.