Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 158

Solve $2a - 5 = 4(3a+1) - 2$ and check.


$
\begin{equation}
\begin{aligned}

2a - 5 =& 4(3a+1) - 2
&& \text{Given equation}
\\
\\
2a-5 =& 12a+4-2
&& \text{Apply Distributive Property}
\\
\\
2a-12a =& 4-2+5
&& \text{Subtract $12a$ and add $5$}
\\
\\
-10a =& 7
&& \text{Simplify}
\\
\\
\frac{\cancel{-10}a}{\cancel{-10}} =& \frac{7}{-10}
&& \text{Divide by } -10
\\
\\
a =& \frac{-7}{10}
&&


\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

2 \left( \frac{-7}{10} \right) - 5 =& 4 \left[ 3 \left( \frac{-7}{10} \right) +1 \right] -2
&& \text{Substitute } a = \frac{-7}{10}
\\
\frac{-7}{5} - 5 =& 4 \left( \frac{-11}{10} \right) - 2
&& \text{Simplify}
\\
\frac{-32}{5} =& \frac{-32}{5}
&&

\end{aligned}
\end{equation}
$