Analyze the work used to write an equivalent equation for:

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

Work shown:

1. Divide both sides by 3:

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

Let's analyze and solve the equation [tex]$ y - 3y = 36 - 5x $[/tex] step-by-step to find an equivalent equation:

1. Combine like terms on the left side of the equation:

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

Simplify the left side by combining like terms:
[tex]\[
y - 3y = -2y
\][/tex]
So the equation now is:
[tex]\[
-2y = 36 - 5x
\][/tex]

2. Solve for [tex]$ y $[/tex]:

To isolate [tex]$ y $[/tex], divide every term in the equation by [tex]$-2$[/tex]:
[tex]\[
y = \frac{36}{-2} - \frac{5x}{-2}
\][/tex]

3. Simplify each term:

Simplify [tex]$\frac{36}{-2}$[/tex]:
[tex]\[
\frac{36}{-2} = -18
\][/tex]

Simplify [tex]$-\frac{5x}{-2}$[/tex]:
[tex]\[
-\frac{5x}{-2} = \frac{5x}{2}
\][/tex]

So, substitute these values back into the equation:
[tex]\[
y = -18 + \frac{5x}{2}
\][/tex]

Rearrange the terms for clarity:
[tex]\[
y = 6 - \frac{5x}{2}
\][/tex]

Thus, the equivalent equation, after solving for [tex]$ y $[/tex], is:
[tex]\[
y = 6 - \frac{5x}{2}
\][/tex]