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

Original 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.

Certainly! Let's go through the process to determine an equivalent equation for [tex]$ y $[/tex] from the original equation [tex]$ 3y = 36 - 5x $[/tex].

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

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

3. Simplify each term:

- On the left side, [tex]$ \frac{3y}{3} $[/tex] simplifies to [tex]$ y $[/tex].
- On the right side:
- [tex]$ \frac{36}{3} $[/tex] simplifies to 12.
- [tex]$ \frac{5x}{3} $[/tex] remains as [tex]$ \frac{5}{3}x $[/tex].

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

Conclusion:
The work involves dividing each term on both sides of the equation by 3 correctly. It is essential to divide both terms on the right side of the equation by 3, not just the constant term 36. This gives:

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

In summary, the original process missed dividing the coefficient of [tex]$ x $[/tex] by 3, which needs to be correctly addressed, resulting in the equation [tex]$ y = 12 - \frac{5}{3}x $[/tex].