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:


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