Answer
$(-\infty,-7]\cup[1,\infty)$
Work Step by Step
The solutions of $|u|\gt c $ are the numbers that satisfy $ u\lt -c $ or $ u\gt c.$
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$|x+3| \geq 4\Rightarrow \left\{\begin{array}{ll}
x+3\leq -4 & \\
or & \\
x+3 \geq 4 &
\end{array}\right.$
$ \begin{array}{lllll}
x+3\leq -4 & /-3 & ...or... & x+3 \geq 4 & /-3\\
x\leq -7 & & & x \geq 1 & \\
x\in(-\infty,-7] & & or & x\in[1,\infty) & \\
& & & &
\end{array} $
Solution set: $(-\infty,-7]\cup[1,\infty)$
