Intermediate Algebra, Chapter 2, 2.7, Section 2.7, Problem 84

Evaluate the equation $|13x| = |2x + 1|$.

This equation is satisfied either if $13x$ and $2x + 1$ are equal to each other or if $13x$ and $2x + 1$ are negatives of each other


$
\begin{equation}
\begin{aligned}

13x =& 2x + 1 && \text{or} &&& 13x =& -(2x + 1)
\\
13 -2x =& 1 && \text{or} &&& 13x + 2x =& -1
\\
11x =& 1 && \text{or} &&& 15x =& -1
\\
x =& \frac{1}{11} && \text{or} &&& x =& - \frac{1}{15}

\end{aligned}
\end{equation}
$


The solution set is $\displaystyle \left \{ - \frac{1}{15}, \frac{1}{11} \right \}$.