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 $\displaystyle \left \{ - \frac{4}{3} \right \}$.