Question

the equation \\(\frac{v}{3} - 4 = -13\\) is solved in several steps below. for each step, choose the reason that best justifies it. step reason \\(\frac{v}{3} - 4 = -13\\) given equation \\(\frac{v}{3} - 4 + 4 = -13 + 4\\) \choose one\ \\(\frac{v}{3} = -9\\) \choose one\ \\(3cdot\frac{v}{3} = -9cdot3\\) \choose one\ \\(v = -27\\) \choose one\

Explanation:

Step1: Add 4 to both sides

$\frac{v}{3} - 4 + 4 = -13 + 4$

Reason: Addition Property of Equality (If $a=b$, then $a+c=b+c$)

Step2: Simplify both sides

$\frac{v}{3} = -9$

Reason: Combine like terms (Arithmetic simplification)

Step3: Multiply both sides by 3

$3 \cdot \frac{v}{3} = -9 \cdot 3$

Reason: Multiplication Property of Equality (If $a=b$, then $a \cdot c=b \cdot c$)

Step4: Simplify both sides

$v = -27$

Reason: Cancel common factors (Arithmetic simplification)

Answer:

1. For $\boldsymbol{\frac{v}{3} - 4 + 4 = -13 + 4}$: Addition Property of Equality
2. For $\boldsymbol{\frac{v}{3} = -9}$: Simplify/Combine like terms
3. For $\boldsymbol{3 \cdot \frac{v}{3} = -9 \cdot 3}$: Multiplication Property of Equality
4. For $\boldsymbol{v = -27}$: Simplify/Cancel common factors