Answer
$(-\infty,-1.7]\cup[0.7,\infty)$
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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$ 5|2x+1|-3\geq 9\qquad $ ... $/+3$
$ 5|2x+1|\geq 12\qquad $ ... $/\div 5$
$|2x+1| \geq 12/5$
$|2x+1| \geq 12/5\Rightarrow \left\{\begin{array}{ll}
2x+1\leq -12/5 & \\
or & \\
2x+1 \geq 12/5 &
\end{array}\right.$
$ \begin{array}{lllll}
2x+1\leq -12/5 & /\times 5 & ...or... & 2x+1 \geq 12/5 & /\times 5\\
10x+5\leq-12 & /-5 & & 10x+5\geq 12 & /-5\\
10x\leq-17 & /\div 10 & & 10x\geq 7 & \\
x\leq-1.7 & & & x\geq 0.7 & \\
x\in(-\infty,-1.7] & & or & x\in[0.7,\infty) & \\
& & & &
\end{array} $
Solution set: $(-\infty,-1.7]\cup[0.7,\infty)$
