College Algebra, Chapter 1, 1.7, Section 1.7, Problem 20

Solve the equation $\displaystyle \left| \frac{3}{5}x + 2 \right| - \frac{1}{2} = 4$


$
\begin{equation}
\begin{aligned}
\left| \frac{3}{5}x + 2 \right| - \frac{1}{2} &= 4\\
\\
\left| \frac{3}{5}x + 2 \right| &= \frac{9}{2} && \text{Subtract 20}
\end{aligned}
\end{equation}
$


We have,

$
\begin{equation}
\begin{aligned}
\frac{3}{5} x + 2 &= \frac{9}{2} && \text{and}& \frac{3}{5}x + 2 &= -\frac{9}{2} && \text{Subtract 2}\\
\\
\frac{3}{5} x &= \frac{5}{2} && \text{and}& \frac{3}{5}x &= - \frac{13}{2} && \text{Multiply each side by 10}\\
\\
6x &= 25 && \text{and}& 6x &= -65 && \text{Divide by 6}\\
\\
x &= \frac{25}{6} && \text{and}& x &= -\frac{65}{6}
\end{aligned}
\end{equation}
$