Beginning Algebra With Applications, Chapter 2, Review Exercises, Section Review Exercises, Problem 22

Simplify $-2[x - 2(x-y)] + 5y$

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