In Gabrielle's first step, she rewrites the original equation \(3 - 5x \cdot 4 = 3\) as \(-5 \cdot 4x = 3\). The property that justifies this step is the Commutative Property of Multiplication.
The Commutative Property states that changing the order of the factors does not change the product. In this case, Gabrielle recognizes that \( -5 \cdot 4x \) can be rearranged to \(-5 \cdot 4 \cdot x\), which maintains the same value. Thus, the justification for her step involves rearranging the multiplication of terms. However, it's important to note that she appears to be simplifying the equation; this change indicates a combination of factoring and algebraic manipulation, but the primary property involved is indeed the commutative property in the multiplication of the coefficients.
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