Intermediate Algebra, Chapter 2, 2.7, Section 2.7, Problem 80

Evaluate the equation $|7x + 12| = |x - 8|$.

This equation is satisfied either if $7x + 12$ and $x - 8$ are equal to each other or if $7x + 12$ and $x - 8$ are negatives of each other


$\begin{equation} \begin{aligned} 7x + 12 =& x - 8 && \text{or} &&& 7x + 12 =& -(x - 8) \\ 7x - x =& -8-12 && \text{or} &&& 7x + x =& 8-12 \\ 6x =& -20 && \text{or} &&& 8x =& -4 \\ x =& - \frac{20}{6} && \text{or} &&& x =& - \frac{4}{8} \\ \\ x =& - \frac{10}{3} && \text{or} &&& x =& - \frac{1}{2} \end{aligned} \end{equation}$


The solution set is $\displaystyle \left \{ - \frac{10}{3}, - \frac{1}{2} \right \}$.