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Answer :
Sure, let's take a step-by-step look at solving the equation [tex]\(3y = 36 - 5x\)[/tex] and determine if the work was done correctly to find an equivalent equation for [tex]\(y\)[/tex].
1. Identify the Equation:
- We start with the equation [tex]\(3y = 36 - 5x\)[/tex].
2. Goal:
- Our objective is to solve for [tex]\(y\)[/tex], meaning we want [tex]\(y\)[/tex] by itself on one side of the equation.
3. Divide Both Sides by 3:
- To isolate [tex]\(y\)[/tex], we divide each term in the equation by 3:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
4. Simplify:
- On the left side, [tex]\(\frac{3y}{3}\)[/tex] simplifies to [tex]\(y\)[/tex].
- On the right side:
- [tex]\(\frac{36}{3}\)[/tex] simplifies to [tex]\(12\)[/tex].
- [tex]\(\frac{5x}{3}\)[/tex] remains as it is because it cannot be simplified further without a given [tex]\(x\)[/tex] value.
5. Final Equivalent Equation:
- After simplifying, the equation becomes:
[tex]\[
y = 12 - \frac{5x}{3}
\][/tex]
6. Conclusion:
- The work is completed correctly. Each term on the right side of the equation was divided by 3 accurately. Therefore, the equivalent equation is [tex]\(y = 12 - \frac{5x}{3}\)[/tex].
Everything here follows the correct mathematical principles for solving the equation and ensures that manipulation maintains equality, confirming the work was performed correctly.
1. Identify the Equation:
- We start with the equation [tex]\(3y = 36 - 5x\)[/tex].
2. Goal:
- Our objective is to solve for [tex]\(y\)[/tex], meaning we want [tex]\(y\)[/tex] by itself on one side of the equation.
3. Divide Both Sides by 3:
- To isolate [tex]\(y\)[/tex], we divide each term in the equation by 3:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
4. Simplify:
- On the left side, [tex]\(\frac{3y}{3}\)[/tex] simplifies to [tex]\(y\)[/tex].
- On the right side:
- [tex]\(\frac{36}{3}\)[/tex] simplifies to [tex]\(12\)[/tex].
- [tex]\(\frac{5x}{3}\)[/tex] remains as it is because it cannot be simplified further without a given [tex]\(x\)[/tex] value.
5. Final Equivalent Equation:
- After simplifying, the equation becomes:
[tex]\[
y = 12 - \frac{5x}{3}
\][/tex]
6. Conclusion:
- The work is completed correctly. Each term on the right side of the equation was divided by 3 accurately. Therefore, the equivalent equation is [tex]\(y = 12 - \frac{5x}{3}\)[/tex].
Everything here follows the correct mathematical principles for solving the equation and ensures that manipulation maintains equality, confirming the work was performed correctly.
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