Answer
$(-\displaystyle \infty,-4]\cup[\frac{1}{2},\infty)$
Work Step by Step
Rewrite as
$|4x+7|\geq 9$
... $|u| \geq c $ is equivalent to ($ u\leq -c $) or ($ u \geq c $)
$ \begin{array}{lllll}
4x+7 \leq-9 & /-7 & ...or... & 4x+7\geq 9 & /-7\\
4x\leq-16 & /\div 4 & & 4x\geq 2 & /\div 4\\
x\leq-4 & & & x\geq 1/2 & \\
x\in(-\infty,-4] & & or & x\in[1/2,\infty) & \\
& & & &
\end{array}$
Solution set: $(-\displaystyle \infty,-4]\cup[\frac{1}{2},\infty)$
