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The equation [tex]$5(3y + 4) = -10$[/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]5(3y + 4) = -10[/tex] & Given equation \\
\hline
[tex]15y + 20 = -10[/tex] & \text{Choose one} \\
\hline
[tex]15y + 20 - 20 = -10 - 20[/tex] & \text{Choose one} \\
\hline
[tex]15y = -30[/tex] & \text{Choose one} \\
\hline
[tex]\frac{15y}{15} = \frac{-30}{15}[/tex] & \text{Choose one} \\
\hline
[tex]y = -2[/tex] & \text{Choose one} \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Certainly! Let's go through each step of the equation [tex]$5(3y + 4) = -10$[/tex] with the appropriate justifications.

1. Step: [tex]\( 5(3y + 4) = -10 \)[/tex]
- Reason: Given equation

2. Step: [tex]\( 15y + 20 = -10 \)[/tex]
- Reason: Distributive property (Distribute the 5 across the parentheses)

3. Step: [tex]\( 15y + 20 - 20 = -10 - 20 \)[/tex]
- Reason: Subtraction property of equality (Subtracting 20 from both sides)

4. Step: [tex]\( 15y = -30 \)[/tex]
- Reason: Simplification (Simplify both sides after combining like terms)

5. Step: [tex]\( \frac{15y}{15} = \frac{-30}{15} \)[/tex]
- Reason: Division property of equality (Dividing both sides by 15)

6. Step: [tex]\( y = -2 \)[/tex]
- Reason: Simplification (Simplify the division on both sides)

So, the completed table with the correct reasons for each step would be:

\begin{tabular}{|c|ll|}
\hline Step & Reason & \\
\hline [tex]$5(3 y+4)=-10$[/tex] & Given equation & \\
\hline [tex]$15 y+20=-10$[/tex] & Distributive property & \\
\hline [tex]$15 y+20-20=-10-20$[/tex] & Subtraction property of equality & \\
\hline [tex]$15 y=-30$[/tex] & Simplification & \\
\hline[tex]$\frac{15 y}{15}=\frac{-30}{15}$[/tex] & Division property of equality & \\
\hline[tex]$y=-2$[/tex] & Simplification & \\
\hline
\end{tabular}

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