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Answer :
To solve the equation [tex]\(3y = 36 - 5x\)[/tex] and write an equivalent equation for [tex]\(y\)[/tex], we need to isolate [tex]\(y\)[/tex]. Here's a step-by-step breakdown of the correct process:
1. Start with the given equation:
[tex]\[
3y = 36 - 5x
\][/tex]
2. Isolate [tex]\(y\)[/tex] by dividing every term in the equation by 3:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
3. Simplify each term:
- The left side becomes [tex]\(y\)[/tex] because [tex]\(\frac{3y}{3} = y\)[/tex].
- The first term on the right becomes 12 because [tex]\(\frac{36}{3} = 12\)[/tex].
- The second term on the right becomes [tex]\(-\frac{5}{3}x\)[/tex] because [tex]\(\frac{5x}{3} = \frac{5}{3}x\)[/tex].
4. Write the simplified equation:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
By following these steps, we can conclude that the work was not initially completed correctly in the problem. The mistake was not dividing both terms on the right side by 3. Both the 36 and the [tex]\(5x\)[/tex] need to be divided by 3 to properly solve for [tex]\(y\)[/tex]. The corrected equivalent equation for [tex]\(y\)[/tex] is [tex]\(y = 12 - \frac{5}{3}x\)[/tex].
1. Start with the given equation:
[tex]\[
3y = 36 - 5x
\][/tex]
2. Isolate [tex]\(y\)[/tex] by dividing every term in the equation by 3:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
3. Simplify each term:
- The left side becomes [tex]\(y\)[/tex] because [tex]\(\frac{3y}{3} = y\)[/tex].
- The first term on the right becomes 12 because [tex]\(\frac{36}{3} = 12\)[/tex].
- The second term on the right becomes [tex]\(-\frac{5}{3}x\)[/tex] because [tex]\(\frac{5x}{3} = \frac{5}{3}x\)[/tex].
4. Write the simplified equation:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
By following these steps, we can conclude that the work was not initially completed correctly in the problem. The mistake was not dividing both terms on the right side by 3. Both the 36 and the [tex]\(5x\)[/tex] need to be divided by 3 to properly solve for [tex]\(y\)[/tex]. The corrected equivalent equation for [tex]\(y\)[/tex] is [tex]\(y = 12 - \frac{5}{3}x\)[/tex].
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