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Answer :
To solve for [tex]\( y \)[/tex] in the given equation [tex]\( 3y = 36 - 5x \)[/tex], you need to isolate [tex]\( y \)[/tex] on one side of the equation. Here's a step-by-step solution:
1. Understand the Goal: We need to rewrite the equation in terms of [tex]\( y \)[/tex], which means [tex]\( y \)[/tex] should be by itself on one side of the equation.
2. Divide Both Sides by 3: To isolate [tex]\( y \)[/tex], divide every term in the equation by 3. This will get rid of the coefficient in front of [tex]\( y \)[/tex].
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
3. Simplify Each Term:
- The left side simplifies to [tex]\( y \)[/tex] because [tex]\( \frac{3y}{3} = y \)[/tex].
- For the right side, divide each term separately:
- [tex]\( \frac{36}{3} = 12 \)[/tex]
- [tex]\( \frac{5x}{3} = \frac{5}{3}x \)[/tex]
4. Write the Simplified Equation:
So the new equation is:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
5. Conclusion: By correctly dividing both sides of the equation by 3, you simplify the expression to solve for [tex]\( y \)[/tex]. This method requires dividing both terms on the right side of the equation, not just the constant term. The work was completed correctly.
This step-by-step approach ensures clarity and correctness in rearranging the equation to solve for [tex]\( y \)[/tex].
1. Understand the Goal: We need to rewrite the equation in terms of [tex]\( y \)[/tex], which means [tex]\( y \)[/tex] should be by itself on one side of the equation.
2. Divide Both Sides by 3: To isolate [tex]\( y \)[/tex], divide every term in the equation by 3. This will get rid of the coefficient in front of [tex]\( y \)[/tex].
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
3. Simplify Each Term:
- The left side simplifies to [tex]\( y \)[/tex] because [tex]\( \frac{3y}{3} = y \)[/tex].
- For the right side, divide each term separately:
- [tex]\( \frac{36}{3} = 12 \)[/tex]
- [tex]\( \frac{5x}{3} = \frac{5}{3}x \)[/tex]
4. Write the Simplified Equation:
So the new equation is:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
5. Conclusion: By correctly dividing both sides of the equation by 3, you simplify the expression to solve for [tex]\( y \)[/tex]. This method requires dividing both terms on the right side of the equation, not just the constant term. The work was completed correctly.
This step-by-step approach ensures clarity and correctness in rearranging the equation to solve for [tex]\( y \)[/tex].
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