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

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

1. Divide both sides by 3:
[tex]
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
[/tex]
[tex]
y = 12 - \frac{5x}{3}
[/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 the equation [tex]$3y = 36 - 5x$[/tex] and write an equivalent equation for [tex]$y$[/tex], we need to isolate [tex]$y$[/tex]. Here's a step-by-step breakdown of the correct process:

1. Start with the given equation:
[tex]\[
3y = 36 - 5x
\][/tex]

2. Isolate [tex]$y$[/tex] by dividing every term in the equation by 3:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]

3. Simplify each term:
- The left side becomes [tex]$y$[/tex] because [tex]$\frac{3y}{3} = y$[/tex].
- The first term on the right becomes 12 because [tex]$\frac{36}{3} = 12$[/tex].
- The second term on the right becomes [tex]$-\frac{5}{3}x$[/tex] because [tex]$\frac{5x}{3} = \frac{5}{3}x$[/tex].

4. Write the simplified equation:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]

By following these steps, we can conclude that the work was not initially completed correctly in the problem. The mistake was not dividing both terms on the right side by 3. Both the 36 and the [tex]$5x$[/tex] need to be divided by 3 to properly solve for [tex]$y$[/tex]. The corrected equivalent equation for [tex]$y$[/tex] is [tex]$y = 12 - \frac{5}{3}x$[/tex].