Intermediate Algebra, Chapter 2, 2.7, Section 2.7, Problem 86

Evaluate the equation $|3x - 1| = |3x + 9|$.

This equation is satisfied either if $3x - 1$ and $3x + 9$ are equal to each other or if $3x - 1$ and $3x + 9$ are negatives of each other


$
\begin{equation}
\begin{aligned}

3x - 1 =& 3x + 9 && \text{or} &&& 3x - 1 =& -(3x + 9)
\\
3x - 3x =& 9 + 1 && \text{or} &&& 3x + 3x =& -9 + 1
\\
0 =& 10 && \text{or} &&& 6x =& -8
\\
& && \text{or} &&& x =& - \frac{4}{3}

\end{aligned}
\end{equation}
$


The solution set is $\displaystyle \left \{ - \frac{4}{3} \right \}$.