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].
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].
