Beginning Algebra With Applications, Chapter 2, 2.2, Section 2.2, Problem 64

Simplify $3y - 12x - 7y + 2y$

$
\begin{equation}
\begin{aligned}
&= 3y + 2y - 7y - 12x && \text{Use the Commutative Property of Addition to rearrange terms}\\
\\
&= (3+2)y - 7y - 12x && \text{Use the Commutative Distributive Property } ba + ca = (b +c) a \\
\\
&= 5y - 7y - 12x && \text{Add coefficient}\\
\\
&= (5 -7)y - 12x && \text{Again, use the Commutative Distributive Property } ba + ca = (b +c) a \\
\\
&= -2y - 12x && \text{Add coefficient}\\
\\
&= -2(y + 6x) && \text{Factor out }-2
\end{aligned}
\end{equation}
$