High School

Analyze the work used to write an equivalent equation for [tex]y[/tex]. What can you conclude about the work?

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]

Options for conclusion:
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]1/12[/tex], not 12.
D. Both terms on the right side need to be divided by 3, not just the 36.

Answer :

To analyze the work used to write an equivalent equation for [tex]\(y\)[/tex] from the given equation [tex]\(3y = 36 - 5x\)[/tex], let's go through the steps involved:

1. Objective: Solve the equation [tex]\(3y = 36 - 5x\)[/tex] for [tex]\(y\)[/tex].

2. Step 1: Divide every term in the equation by 3 to isolate [tex]\(y\)[/tex]. This means we perform the division on each term separately.

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

3. Simplification:

- The left side simplifies to [tex]\(y\)[/tex], because [tex]\(\frac{3y}{3} = y\)[/tex].
- The first term on the right side is [tex]\(\frac{36}{3}\)[/tex], which simplifies to 12, because 36 divided by 3 is 12.
- The second term on the right side, [tex]\(\frac{5x}{3}\)[/tex], remains as [tex]\(\frac{5}{3}x\)[/tex].

4. Conclusion:

By simplifying the equation, we get:

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

The analysis shows that the original work to solve for [tex]\(y\)[/tex] was completed correctly and option 1 ("The work was completed correctly.") accurately describes the appropriate method. Therefore, the conclusion is that dividing all the terms by 3 was the correct step to isolate [tex]\(y\)[/tex].