Analyze the work used to write an equivalent equation for [tex]y[/tex].

Given:
\[3y = 36 - 5x\]

1. Divide both sides by 3:
\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\]
\[
y = 12 - \frac{5x}{3}
\]

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 \(\frac{1}{12}\), not 12.

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

Let's analyze the process of simplifying the given equation. The original equation is:

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

We are tasked with solving for [tex]\( y \)[/tex]. The suggested first step is to divide both sides of the equation by 3 to isolate [tex]\( y \)[/tex]:

1. Divide both sides by 3:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]

- The left side simplifies as follows:
[tex]\[
\frac{3y}{3} = y
\][/tex]

- For the right side, divide each term individually:
[tex]\[
\frac{36}{3} = 12 \quad \text{and} \quad \frac{5x}{3} = \frac{5x}{3}
\][/tex]

2. Simplified equation:
[tex]\[
y = 12 - \frac{5x}{3}
\][/tex]

Upon reviewing each step, we can conclude:

- Both sides of the equation were correctly divided by 3.
- Each term on the right side was divided by 3 as needed.

Thus, the work was completed correctly in writing the equivalent equation for [tex]\( y \)[/tex].