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Answer :
Let's go through the steps to determine if the equation for [tex]\( y \)[/tex] was solved correctly.
We start with the original equation:
[tex]\[ 3y = 36 - 5x \][/tex]
To solve for [tex]\( y \)[/tex], we need to isolate it on one side of the equation. We do this by dividing every term in the equation by 3. Let's break it down:
1. Divide both sides of the equation by 3:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
2. Simplify each part:
- The left side becomes:
[tex]\[
y
\][/tex]
- The term [tex]\(\frac{36}{3}\)[/tex] on the right side simplifies to:
[tex]\[
12
\][/tex]
- The term [tex]\(\frac{5x}{3}\)[/tex] remains:
[tex]\[
\frac{5}{3}x
\][/tex]
3. Write the final equation:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
The division was applied correctly to every term of the equation, giving us the equivalent equation [tex]\( y = 12 - \frac{5}{3}x \)[/tex].
Therefore, we can conclude: The work was completed correctly.
We start with the original equation:
[tex]\[ 3y = 36 - 5x \][/tex]
To solve for [tex]\( y \)[/tex], we need to isolate it on one side of the equation. We do this by dividing every term in the equation by 3. Let's break it down:
1. Divide both sides of the equation by 3:
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
2. Simplify each part:
- The left side becomes:
[tex]\[
y
\][/tex]
- The term [tex]\(\frac{36}{3}\)[/tex] on the right side simplifies to:
[tex]\[
12
\][/tex]
- The term [tex]\(\frac{5x}{3}\)[/tex] remains:
[tex]\[
\frac{5}{3}x
\][/tex]
3. Write the final equation:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
The division was applied correctly to every term of the equation, giving us the equivalent equation [tex]\( y = 12 - \frac{5}{3}x \)[/tex].
Therefore, we can conclude: The work was completed correctly.
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