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

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

Steps to solve:

1. Divide both sides by 3:
[tex]\[

\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}

\][/tex]

Simplifies to:
[tex]\[

y = 12 - \frac{5x}{3}

\][/tex]

Which statement is correct?

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 analyze the work used to rewrite the equation [tex]$3y = 36 - 5x$[/tex] into an equivalent equation for [tex]$y$[/tex], let's carefully go through the steps:

1. Given Equation:
The original equation is [tex]$3y = 36 - 5x$[/tex].

2. Dividing Both Sides by 3:
To solve for [tex]$y$[/tex], you need to isolate it on one side of the equation. Start by dividing every term on both sides of the equation by 3:

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

3. Simplifying the Equation:
- The left side simplifies to [tex]$y$[/tex].
- On the right side, you divide each term separately:
[tex]$\frac{36}{3} = 12$[/tex]
[tex]$\frac{5x}{3} = \frac{5}{3}x$[/tex]

So, the equation simplifies to:

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

4. Conclusion:
- The solution was completed correctly. The calculation of dividing each term individually by 3 and simplifying them was done accurately.
- The misunderstanding mentioned about [tex]$36$[/tex] being divided by 3 to yield [tex]$1/12$[/tex] is incorrect. The correct division should result in [tex]$12$[/tex].
- It was correctly noted that both terms on the right side, [tex]$36$[/tex] and [tex]$5x$[/tex], need to be divided by 3.

This leads us to the correct and simplified equation:

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