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The equation [tex]$8(x+2)=-32$[/tex] is solved in several steps below. For each step, choose the reason that best justifies it.

\begin{tabular}{|c|l|}
\hline
Step & Reason \\
\hline
[tex]$8(x+2)=-32$[/tex] & Given equation \\
\hline
[tex][tex]$8x+16=-32$[/tex][/tex] & Distributive Property \\
\hline
[tex]$8x+16-16=-32-16$[/tex] & Subtraction Property of Equality \\
\hline
[tex]$8x=-48$[/tex] & Simplification \\
\hline
[tex]\frac{8x}{8}=\frac{-48}{8}$[/tex] & Division Property of Equality \\
\hline
[tex]$x=-6$[/tex] & Simplification \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Certainly! Let's solve the equation [tex]\(8(x+2) = -32\)[/tex] step-by-step and choose the appropriate reasons for each step.

### Step-by-Step Solution

1. Given equation:
[tex]\[ 8(x + 2) = -32 \][/tex]
Reason: This is the given equation.

2. Apply the Distributive Property:
[tex]\[ 8x + 16 = -32 \][/tex]
Reason: Distributive Property. The distributive property is used to multiply 8 with both [tex]\(x\)[/tex] and 2.

3. Subtract 16 from both sides:
[tex]\[ 8x + 16 - 16 = -32 - 16 \][/tex]
Reason: Subtract 16 from both sides. This step is done to isolate the term containing [tex]\(x\)[/tex] on one side of the equation.

4. Simplify both sides:
[tex]\[ 8x = -48 \][/tex]
Reason: Simplify both sides. Simplifying [tex]\(+16 - 16\)[/tex] on the left-hand side and [tex]\(-32 - 16\)[/tex] on the right-hand side.

5. Divide both sides by 8:
[tex]\[ \frac{8x}{8} = \frac{-48}{8} \][/tex]
Reason: Divide both sides by 8. This step is done to solve for [tex]\(x\)[/tex] by getting rid of the coefficient 8.

6. Simplify both sides after division:
[tex]\[ x = -6 \][/tex]
Reason: Simplify both sides after division. The division simplifies to [tex]\(x = -6\)[/tex].

### Filled-in Table

\begin{tabular}{|c|l|}
\hline
Step & Reason \\
\hline
[tex]$8(x+2) = -32$[/tex] & Given equation \\
\hline
[tex]$8x + 16 = -32$[/tex] & Distributive Property \\
\hline
[tex]$8x + 16 - 16 = -32 - 16$[/tex] & Subtract 16 from both sides \\
\hline
[tex]$8x = -48$[/tex] & Simplify both sides \\
\hline
[tex]$\frac{8x}{8} = \frac{-48}{8}$[/tex] & Divide both sides by 8 \\
\hline
[tex]$x = -6$[/tex] & Simplify both sides after division \\
\hline
\end{tabular}

This detailed solution walks you through each step clearly, ensuring that you understand the rationale for each operation performed.

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