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------------------------------------------------ Analyze the work used to write an equivalent equation for [tex] y [/tex] from the given equation:

[tex] 3y = 36 - 5x [/tex]

1. Divide both sides by 3:

[tex]
\begin{aligned}
\frac{3y}{3} & = \frac{36}{3} - \frac{5x}{3} \\
y & = 12 - \frac{5x}{3}
\end{aligned}
[/tex]

What can you conclude about the work?

A. The work was completed correctly.

B. Both sides needed to be multiplied by 3, rather than divided by 3.

C. When dividing 36 by 3, the answer should have been [tex] \frac{1}{12} [/tex], not 12.

D. Both terms on the right side need to be divided by 3, not just the 36.

To solve for [tex]\( y \)[/tex] in the given equation [tex]\( 3y = 36 - 5x \)[/tex], you need to isolate [tex]\( y \)[/tex] on one side of the equation. Here's a step-by-step solution:

1. Understand the Goal: We need to rewrite the equation in terms of [tex]\( y \)[/tex], which means [tex]\( y \)[/tex] should be by itself on one side of the equation.

2. Divide Both Sides by 3: To isolate [tex]\( y \)[/tex], divide every term in the equation by 3. This will get rid of the coefficient in front of [tex]\( y \)[/tex].

[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]

3. Simplify Each Term:
- The left side simplifies to [tex]\( y \)[/tex] because [tex]\( \frac{3y}{3} = y \)[/tex].
- For the right side, divide each term separately:
- [tex]\( \frac{36}{3} = 12 \)[/tex]
- [tex]\( \frac{5x}{3} = \frac{5}{3}x \)[/tex]

4. Write the Simplified Equation:
So the new equation is:

[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]

5. Conclusion: By correctly dividing both sides of the equation by 3, you simplify the expression to solve for [tex]\( y \)[/tex]. This method requires dividing both terms on the right side of the equation, not just the constant term. The work was completed correctly.

This step-by-step approach ensures clarity and correctness in rearranging the equation to solve for [tex]\( y \)[/tex].