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Answer :
To analyze the work used to write an equivalent equation for [tex]\( y \)[/tex] from the equation [tex]\( 3y = 36 - 5x \)[/tex], let's break down the steps:
1. Start with the original equation:
[tex]\[
3y = 36 - 5x
\][/tex]
2. Divide every term of the equation by 3. This step is necessary to isolate [tex]\( y \)[/tex]. When dividing both sides of the equation by 3, you get:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
3. Simplify each term:
- On the left side, [tex]\( \frac{3y}{3} = y \)[/tex].
- On the right side, [tex]\( \frac{36}{3} = 12 \)[/tex] and [tex]\( \frac{5x}{3} = \frac{5x}{3} \)[/tex].
4. Rewrite the simplified equation:
[tex]\[
y = 12 - \frac{5x}{3}
\][/tex]
5. Conclusion about the work:
The steps performed were correct with respect to the method used: dividing all terms by 3. Thus, the equivalent equation is [tex]\( y = 12 - \frac{5x}{3} \)[/tex].
Therefore, the operation of dividing all terms on both sides by 3 is correctly applied, and the rewritten equation is valid. The work was completed correctly.
1. Start with the original equation:
[tex]\[
3y = 36 - 5x
\][/tex]
2. Divide every term of the equation by 3. This step is necessary to isolate [tex]\( y \)[/tex]. When dividing both sides of the equation by 3, you get:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
3. Simplify each term:
- On the left side, [tex]\( \frac{3y}{3} = y \)[/tex].
- On the right side, [tex]\( \frac{36}{3} = 12 \)[/tex] and [tex]\( \frac{5x}{3} = \frac{5x}{3} \)[/tex].
4. Rewrite the simplified equation:
[tex]\[
y = 12 - \frac{5x}{3}
\][/tex]
5. Conclusion about the work:
The steps performed were correct with respect to the method used: dividing all terms by 3. Thus, the equivalent equation is [tex]\( y = 12 - \frac{5x}{3} \)[/tex].
Therefore, the operation of dividing all terms on both sides by 3 is correctly applied, and the rewritten equation is valid. The work was completed correctly.
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