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Answer :
Let's analyze the problem and walk through the steps to solve the given equation for [tex]\( y \)[/tex].
1. Given Equation:
[tex]\[
3y = 36 - 5x
\][/tex]
2. Goal: Solve for [tex]\( y \)[/tex].
3. Divide both sides by 3 to isolate [tex]\( y \)[/tex]:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
4. Simplify each term:
- On the left side, [tex]\(\frac{3y}{3} = y\)[/tex].
- On the right side:
- [tex]\(\frac{36}{3} = 12\)[/tex]
- [tex]\(\frac{5x}{3} = \frac{5}{3}x\)[/tex]
5. Write the equivalent equation:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
Conclusion: The work was completed correctly. When dividing the right side, both terms ([tex]\(36\)[/tex] and [tex]\(5x\)[/tex]) should be divided by [tex]\(3\)[/tex]. This results in the simplified equation of [tex]\( y = 12 - \frac{5}{3}x \)[/tex]. There's no need for multiplication; only division was necessary to isolate [tex]\( y \)[/tex].
1. Given Equation:
[tex]\[
3y = 36 - 5x
\][/tex]
2. Goal: Solve for [tex]\( y \)[/tex].
3. Divide both sides by 3 to isolate [tex]\( y \)[/tex]:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
4. Simplify each term:
- On the left side, [tex]\(\frac{3y}{3} = y\)[/tex].
- On the right side:
- [tex]\(\frac{36}{3} = 12\)[/tex]
- [tex]\(\frac{5x}{3} = \frac{5}{3}x\)[/tex]
5. Write the equivalent equation:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
Conclusion: The work was completed correctly. When dividing the right side, both terms ([tex]\(36\)[/tex] and [tex]\(5x\)[/tex]) should be divided by [tex]\(3\)[/tex]. This results in the simplified equation of [tex]\( y = 12 - \frac{5}{3}x \)[/tex]. There's no need for multiplication; only division was necessary to isolate [tex]\( y \)[/tex].
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