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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.

Answer :

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].

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