When solving an equation, Gabriel's first step is shown below. Which property justifies Gabriel's first step? Original equation: -4(x+-2)=2 first step: -4x+8=2

Answer 1

Gabriel's first step in the equation \(-4(x + -2) = 2\) transforming it to \(-4x + 8 = 2\) is justified by the Distributive Property.

The Distributive Property states that for any three numbers \(a\), \(b\), and \(c\):

\[ a(b + c) = ab + ac \]

In Gabriel’s case, he applied the Distributive Property by distributing \(-4\) to both \(x\) and \(-2\):

\[ -4(x + -2) = -4x + (-4)(-2) = -4x + 8 \]

Thus, the justification for Gabriel's first step is indeed the Distributive Property.