Intermediate Algebra, Chapter 2, 2.7, Section 2.7, Problem 70

Solve the equation $|x + 5| -2 = 12$.


$\begin{equation} \begin{aligned} |x + 5| -2 =& 12 \\ |x + 5| =& 14 \end{aligned} \end{equation}$


We can solve this compound equation as follows


$\begin{equation} \begin{aligned} x + 5 =& 14 && \text{or} &&& x + 5 =& -14 && \\ x =& 9 && \text{or} &&& x =& -19 && \text{Subtract each side by } 5 \end{aligned} \end{equation}$


The solution set is $\{ -19,9 \}$.