Intermediate Algebra, Chapter 2, 2.7, Section 2.7, Problem 18

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

We can solve this compound equation as follows


$
\begin{equation}
\begin{aligned}

\frac{2}{3}x - 1 =& 5 && \qquad \text{or} &&& \frac{2}{3}x - 1 =& -5
&&
\\
\\
\frac{2}{3}x =& 6 && \qquad \text{or} &&& \frac{2}{3}x =& -4
&& \text{Add } 1
\\
\\
x =& \frac{18}{2} && \qquad \text{or} &&& x =& \frac{-12}{2}
&& \text{Multiply } \frac{3}{2}
\\
\\
x =& 9 &&\qquad \text{or} &&& x =& -6
&& \text{Reduce to lowest terms}

\end{aligned}
\end{equation}
$



The solution set is $\{ -6,9 \}$.