Answer :
To analyze the work used to rewrite the equation [tex]\(3y = 36 - 5x\)[/tex] into an equivalent equation for [tex]\(y\)[/tex], let's carefully go through the steps:
1. Given Equation:
The original equation is [tex]\(3y = 36 - 5x\)[/tex].
2. Dividing Both Sides by 3:
To solve for [tex]\(y\)[/tex], you need to isolate it on one side of the equation. Start by dividing every term on both sides of the equation by 3:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
3. Simplifying the Equation:
- The left side simplifies to [tex]\(y\)[/tex].
- On the right side, you divide each term separately:
[tex]\(\frac{36}{3} = 12\)[/tex]
[tex]\(\frac{5x}{3} = \frac{5}{3}x\)[/tex]
So, the equation simplifies to:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
4. Conclusion:
- The solution was completed correctly. The calculation of dividing each term individually by 3 and simplifying them was done accurately.
- The misunderstanding mentioned about [tex]\(36\)[/tex] being divided by 3 to yield [tex]\(1/12\)[/tex] is incorrect. The correct division should result in [tex]\(12\)[/tex].
- It was correctly noted that both terms on the right side, [tex]\(36\)[/tex] and [tex]\(5x\)[/tex], need to be divided by 3.
This leads us to the correct and simplified equation:
[tex]\[ y = 12 - \frac{5}{3}x \][/tex]
1. Given Equation:
The original equation is [tex]\(3y = 36 - 5x\)[/tex].
2. Dividing Both Sides by 3:
To solve for [tex]\(y\)[/tex], you need to isolate it on one side of the equation. Start by dividing every term on both sides of the equation by 3:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
3. Simplifying the Equation:
- The left side simplifies to [tex]\(y\)[/tex].
- On the right side, you divide each term separately:
[tex]\(\frac{36}{3} = 12\)[/tex]
[tex]\(\frac{5x}{3} = \frac{5}{3}x\)[/tex]
So, the equation simplifies to:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
4. Conclusion:
- The solution was completed correctly. The calculation of dividing each term individually by 3 and simplifying them was done accurately.
- The misunderstanding mentioned about [tex]\(36\)[/tex] being divided by 3 to yield [tex]\(1/12\)[/tex] is incorrect. The correct division should result in [tex]\(12\)[/tex].
- It was correctly noted that both terms on the right side, [tex]\(36\)[/tex] and [tex]\(5x\)[/tex], need to be divided by 3.
This leads us to the correct and simplified equation:
[tex]\[ y = 12 - \frac{5}{3}x \][/tex]