Beginning Algebra With Applications, Chapter 2, 2.2, Section 2.2, Problem 178

Simplify $\displaystyle -\frac{1}{4} [2x + 2(y -6y)]$

$
\begin{equation}
\begin{aligned}
&= -\frac{1}{4} [2x + 2(y) - 2(6y)] && \text{Use the Distributive Property}\\
\\
&= -\frac{1}{4} [2x + 2(y) - (2 \cdot 6) y] && \text{Use the Associative Property of Multiplication to group factors}\\
\\
&= -\frac{1}{4} [2x + 2y - 12y] && \text{Simplify}\\
\\
&= -\frac{1}{4} [2x - 10y] && \text{Combine like terms}\\
\\
&= -\frac{1}{4} (2x) - \left( -\frac{1}{4} \right) (10y) && \text{Again, use the Distributive Property}\\
\\
&= \left(\left( -\frac{1}{4} \right) \cdot 2 \right) x + \left( \frac{1}{4} \cdot 10 \right)y && \text{Again, by using the Associative Property of Multiplication to group factors }\\
\\
&= -\frac{2}{4}x + \frac{10}{4}y && \text{Evaluate}\\
\\
&= -\frac{1}{2}x + \frac{5}{2}y && \text{Simplify}
\end{aligned}
\end{equation}
$

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