Calculate: |u+4| > 6

Expression: $|u+4| > 6$

Separate the inequality into $2$ possible cases

$\begin{array} { l }\begin{array} { l }u+4 > 6,& u+4 \geq 0\end{array},\\\begin{array} { l }-\left( u+4 \right) > 6,& u+4 < 0\end{array}\end{array}$

Solve the inequality for $u$

$\begin{array} { l }\begin{array} { l }u > 2,& u+4 \geq 0\end{array},\\\begin{array} { l }-\left( u+4 \right) > 6,& u+4 < 0\end{array}\end{array}$

Solve the inequality for $u$

$\begin{array} { l }\begin{array} { l }u > 2,& u \geq -4\end{array},\\\begin{array} { l }-\left( u+4 \right) > 6,& u+4 < 0\end{array}\end{array}$

Solve the inequality for $u$

$\begin{array} { l }\begin{array} { l }u > 2,& u \geq -4\end{array},\\\begin{array} { l }u < -10,& u+4 < 0\end{array}\end{array}$

Solve the inequality for $u$

$\begin{array} { l }\begin{array} { l }u > 2,& u \geq -4\end{array},\\\begin{array} { l }u < -10,& u < -4\end{array}\end{array}$

Find the intersection

$\begin{array} { l }u \in \langle2, +\infty\rangle,\\\begin{array} { l }u < -10,& u < -4\end{array}\end{array}$

Find the intersection

$\begin{array} { l }u \in \langle2, +\infty\rangle,\\u \in \langle-\infty, -10\rangle\end{array}$

Find the union

$u \in \langle-\infty, -10\rangle \cup \langle2, +\infty\rangle$