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 $\{ -19,9 \}$.