Answer :
Let's analyze the given linear equation and the solution steps for errors:
Original Equation:
[tex]\[ 3y = 36 - 5x \][/tex]
1. Divide both sides by 3: The goal is to isolate [tex]\( y \)[/tex].
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
- When dividing [tex]\( 3y \)[/tex] by 3, you get [tex]\( y \)[/tex].
- When dividing [tex]\( 36 \)[/tex] by 3, you get 12.
- Do not forget to divide the entire expression on the right side by 3, not just the constant. So [tex]\( 5x \)[/tex] should also be divided by 3.
Simplified equation:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
Conclusion:
- The original solution where [tex]\( y = 12 - 5x \)[/tex] was claimed is incorrect because [tex]\( 5x \)[/tex] should have been divided by 3 as well.
- The correct final form of the equation should be [tex]\( y = 12 - \frac{5}{3}x \)[/tex].
- Both terms on the right side needed to be divided properly to maintain equation balance.
The work needed correct attention to detail when performing operations across the entire equation.
Original Equation:
[tex]\[ 3y = 36 - 5x \][/tex]
1. Divide both sides by 3: The goal is to isolate [tex]\( y \)[/tex].
[tex]\[
\frac{3y}{3} = \frac{36}{3} - \frac{5x}{3}
\][/tex]
- When dividing [tex]\( 3y \)[/tex] by 3, you get [tex]\( y \)[/tex].
- When dividing [tex]\( 36 \)[/tex] by 3, you get 12.
- Do not forget to divide the entire expression on the right side by 3, not just the constant. So [tex]\( 5x \)[/tex] should also be divided by 3.
Simplified equation:
[tex]\[
y = 12 - \frac{5}{3}x
\][/tex]
Conclusion:
- The original solution where [tex]\( y = 12 - 5x \)[/tex] was claimed is incorrect because [tex]\( 5x \)[/tex] should have been divided by 3 as well.
- The correct final form of the equation should be [tex]\( y = 12 - \frac{5}{3}x \)[/tex].
- Both terms on the right side needed to be divided properly to maintain equation balance.
The work needed correct attention to detail when performing operations across the entire equation.
