Question

the equation $-7(v - 4) = 49$ is solved in several steps below. for each step, choose the reason that best justifies it. step reason $-7(v - 4) = 49$ given equation $-7v + 28 = 49$ addition property of equality $-7v + 28 - 28 = 49 - 28$ subtraction property of equality $-7v = 21$ simplifying $\frac{-7v}{-7} = \frac{21}{-7}$ division property of equality $v = -3$ simplifying

Explanation:

Step1: Recall the Distributive Property

The Distributive Property states that \(a(b - c)=ab - ac\). Here, \(a=-7\), \(b = v\), and \(c = 4\), so \(-7(v - 4)=-7\times v-(-7)\times4=-7v + 28\).

Step2: Analyze the given reason

The Addition Property of Equality is about adding the same number to both sides of an equation, which is not what's happening here. The transformation from \(-7(v - 4)=49\) to \(-7v + 28 = 49\) is due to distributing \(-7\) over \((v - 4)\), so the correct reason is the Distributive Property.

Answer:

The correct reason for the step \(-7v + 28 = 49\) is the Distributive Property (not Addition Property of Equality).