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Answer :
To analyze the equation and determine what went wrong, let's consider the original equation:
[tex]\[ 3y = 36 - 5x \][/tex]
To solve for [tex]\( y \)[/tex], you need to simplify both sides of the equation by dividing every term by 3. Let's do this step-by-step:
1. Divide Every Term by 3:
- The left side of the equation is [tex]\( 3y \)[/tex]. When you divide [tex]\( 3y \)[/tex] by 3, you get [tex]\( y \)[/tex].
- On the right side, you have two terms: [tex]\( 36 \)[/tex] and [tex]\( -5x \)[/tex]. You need to divide both terms separately by 3:
[tex]\[
36 \div 3 = 12
\][/tex]
[tex]\[
\frac{-5x}{3} = -\frac{5}{3}x
\][/tex]
2. Write the Equation for [tex]\( y \)[/tex]:
- Once both terms on the right side are divided by 3, you get:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
Conclusion: The step to solve for [tex]\( y \)[/tex] should include dividing both terms on the right side by 3. The correct version of solving the equation is:
[tex]\[ y = 12 - \frac{5}{3}x \][/tex]
Thus, the conclusion is that both terms on the right side need to be divided by 3, not just the 36. The work in your problem was not completed correctly initially because dividing was not applied to each term separately.
[tex]\[ 3y = 36 - 5x \][/tex]
To solve for [tex]\( y \)[/tex], you need to simplify both sides of the equation by dividing every term by 3. Let's do this step-by-step:
1. Divide Every Term by 3:
- The left side of the equation is [tex]\( 3y \)[/tex]. When you divide [tex]\( 3y \)[/tex] by 3, you get [tex]\( y \)[/tex].
- On the right side, you have two terms: [tex]\( 36 \)[/tex] and [tex]\( -5x \)[/tex]. You need to divide both terms separately by 3:
[tex]\[
36 \div 3 = 12
\][/tex]
[tex]\[
\frac{-5x}{3} = -\frac{5}{3}x
\][/tex]
2. Write the Equation for [tex]\( y \)[/tex]:
- Once both terms on the right side are divided by 3, you get:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
Conclusion: The step to solve for [tex]\( y \)[/tex] should include dividing both terms on the right side by 3. The correct version of solving the equation is:
[tex]\[ y = 12 - \frac{5}{3}x \][/tex]
Thus, the conclusion is that both terms on the right side need to be divided by 3, not just the 36. The work in your problem was not completed correctly initially because dividing was not applied to each term separately.
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