Analyze the work used to write an equivalent equation for [tex]$ y $[/tex] in the equation [tex]$ 3y = 36 - 5x $[/tex]. What can you conclude about the work?

- The work was completed correctly.
- Both sides needed to be multiplied by 3, rather than divided by 3.
- When dividing 36 by 3, the answer should have been 12, not [tex]$ 1/12 $[/tex].

Correct solution steps:

1. Divide both sides by 3:

[tex]\[

\begin{aligned}

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

y &= 12 - 5x

\end{aligned}

\][/tex]

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

Let's analyze the process of writing an equivalent equation for [tex]$ y $[/tex] from the given equation [tex]$ 3y = 36 - 5x $[/tex].

Step 1: The goal is to solve for [tex]$ y $[/tex]. To do this, we need to isolate [tex]$ y $[/tex] on one side of the equation.

Step 2: Since [tex]$ y $[/tex] is currently being multiplied by 3 in the equation, we divide every term in the equation by 3 to cancel out the coefficient in front of [tex]$ y $[/tex].

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

Step 3: Simplify the equation:

- The left side simplifies to [tex]$ y $[/tex].
- The right side involves two terms: [tex]$ \frac{36}{3} $[/tex] and [tex]$ \frac{5x}{3} $[/tex].

- Divide 36 by 3 to get 12.
- The term [tex]$ -5x $[/tex] divided by 3 becomes [tex]$-\frac{5}{3}x$[/tex].

Thus, we have:

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

Conclusion: The process was completed correctly. Both terms on the right side of the original equation were divided by 3 to isolate [tex]$ y $[/tex], which is the appropriate method to find the equivalent equation. The resulting equation is [tex]$ y = 12 - \frac{5}{3}x $[/tex].