Answer :
Sure! Let's solve the equation step-by-step and identify any errors in the student's solution.
The original equation is:
[tex]\[ 0.15(y - 0.2) = 2 - 0.5(1 - y) \][/tex]
Step 1: Distribute the numbers inside the parentheses.
For the left side:
[tex]\[ 0.15(y - 0.2) = 0.15y - 0.03 \][/tex]
For the right side:
[tex]\[ 2 - 0.5(1 - y) = 2 - 0.5 + 0.5y \][/tex]
[tex]\[ 2 - 0.5 + 0.5y = 1.5 + 0.5y \][/tex]
So, the equation simplifies to:
[tex]\[ 0.15y - 0.03 = 1.5 + 0.5y \][/tex]
Step 2: Move all terms involving 'y' to one side and constants to the other side.
We can subtract [tex]\(0.5y\)[/tex] from both sides to isolate the variable [tex]\(y\)[/tex]:
[tex]\[ 0.15y - 0.03 - 0.5y = 1.5 + 0.5y - 0.5y \][/tex]
[tex]\[ -0.35y - 0.03 = 1.5 \][/tex]
Next, add [tex]\(0.03\)[/tex] to both sides to move the constant term:
[tex]\[ -0.35y - 0.03 + 0.03 = 1.5 + 0.03 \][/tex]
[tex]\[ -0.35y = 1.53 \][/tex]
Step 3: Divide both sides by -0.35 to solve for 'y'.
[tex]\[ y = \frac{1.53}{-0.35} \][/tex]
Step 4: Perform the division.
[tex]\[ y = -4.371428571428572 \][/tex]
So, the corrected solution shows that the student should have come to the final answer:
[tex]\[ y = -4.371428571428572 \][/tex]
The error the student made was:
1. Incorrectly distributing values when removing parentheses.
2. Introducing an unnecessary step by multiplying both sides by 100, which complicated the process.
The correct steps should involve simplifying the terms correctly and solving for [tex]\( y \)[/tex] straightforwardly as shown above.
The original equation is:
[tex]\[ 0.15(y - 0.2) = 2 - 0.5(1 - y) \][/tex]
Step 1: Distribute the numbers inside the parentheses.
For the left side:
[tex]\[ 0.15(y - 0.2) = 0.15y - 0.03 \][/tex]
For the right side:
[tex]\[ 2 - 0.5(1 - y) = 2 - 0.5 + 0.5y \][/tex]
[tex]\[ 2 - 0.5 + 0.5y = 1.5 + 0.5y \][/tex]
So, the equation simplifies to:
[tex]\[ 0.15y - 0.03 = 1.5 + 0.5y \][/tex]
Step 2: Move all terms involving 'y' to one side and constants to the other side.
We can subtract [tex]\(0.5y\)[/tex] from both sides to isolate the variable [tex]\(y\)[/tex]:
[tex]\[ 0.15y - 0.03 - 0.5y = 1.5 + 0.5y - 0.5y \][/tex]
[tex]\[ -0.35y - 0.03 = 1.5 \][/tex]
Next, add [tex]\(0.03\)[/tex] to both sides to move the constant term:
[tex]\[ -0.35y - 0.03 + 0.03 = 1.5 + 0.03 \][/tex]
[tex]\[ -0.35y = 1.53 \][/tex]
Step 3: Divide both sides by -0.35 to solve for 'y'.
[tex]\[ y = \frac{1.53}{-0.35} \][/tex]
Step 4: Perform the division.
[tex]\[ y = -4.371428571428572 \][/tex]
So, the corrected solution shows that the student should have come to the final answer:
[tex]\[ y = -4.371428571428572 \][/tex]
The error the student made was:
1. Incorrectly distributing values when removing parentheses.
2. Introducing an unnecessary step by multiplying both sides by 100, which complicated the process.
The correct steps should involve simplifying the terms correctly and solving for [tex]\( y \)[/tex] straightforwardly as shown above.
