Question

When solving an equation, Drew's first step is shown below. Which property justifies Drew's first step?
Original Equation:
Original Equation:
minus, 5, left parenthesis, minus, 5, x, right parenthesis, equals, 3
−5(−5x)=
3
First Step:
First Step:
left parenthesis, minus, 5, dot, minus, 5, right parenthesis, x, equals, 3
(−5⋅−5)x=
3

Answer 1

Drew's first step involves rewriting the original equation from \(-5(-5x) = 3\) to \((-5 \cdot -5)x = 3\). The property that justifies this first step is the **Associative Property of Multiplication**. This property allows us to rearrange the grouping of the factors being multiplied without changing the product.

In this case, \(-5(-5x)\) is rewritten as \((-5 \cdot -5)x\), which shows that the multiplication of \(-5\) and the term \(-5x\) can be separated and rearranged.

So, in summary, the property used is the **Associative Property of Multiplication**.