Answer
$x=12,\quad x=-19$
Work Step by Step
Given \begin{equation}
|2 x+7|=31.
\end{equation} The solution of the absolute value equation is the following:
\begin{equation}
\begin{aligned}
2 x+7& =31 & \text { or } & & 2 x+7 & =-31 \\
x & =\frac{31-7}{2} & & & x & =\frac{-31-7}{2}\\
x & =12 & \text { or } & & x & =-19\\
\end{aligned}
\end{equation} The solution is
\begin{equation}
x=12,\quad x=-19.
\end{equation}
