Question

describe and correct any error a student may have made when solving the equation ( 0.15(y - 0.2)=2 - 0.5(1 - y) ).

the student first made an error when writing ( 0.15y - 0.3=2 - 0.5 + 0.5y ). the expression on the left side of that equation should be ( -0.03 ). the correct answer is ( y=\frac{-153}{35} ).
(simplify your answers.)

Explanation:

Step1: Expand the left - hand side

When expanding \(0.15(y - 0.2)\) using the distributive property \(a(b - c)=ab - ac\), we have \(0.15\times y-0.15\times0.2=0.15y - 0.03\), not \(0.15y-0.3\).

Step2: Expand the right - hand side

Expand \(2-0.5(1 - y)\) using the distributive property \(a(b - c)=ab - ac\). We get \(2-(0.5\times1-0.5\times y)=2 - 0.5+0.5y=1.5 + 0.5y\).

Step3: Solve the corrected equation

The corrected equation is \(0.15y-0.03 = 1.5+0.5y\).
Subtract \(0.15y\) from both sides: \(0.15y-0.15y - 0.03=1.5+0.5y-0.15y\), which simplifies to \(- 0.03=1.5 + 0.35y\).
Subtract \(1.5\) from both sides: \(-0.03 - 1.5=1.5-1.5 + 0.35y\), so \(-1.53 = 0.35y\).
Divide both sides by \(0.35\): \(y=\frac{-1.53}{0.35}=-\frac{153}{35}\).

Answer:

The student made an error in the distribution of \(0.15\) on the left - hand side. The correct value after distributing \(0.15\) in \(0.15(y - 0.2)\) is \(0.15y-0.03\). The correct answer is \(y =-\frac{153}{35}\).