Answer
$(-\infty,-2]\cup[7,\infty)$
See graph.
Work Step by Step
Step 1. Remove the absolute value sign and transform the original inequality:
$|2x-5|\ge9\Longrightarrow 2x-5\le-9\ or\ 2x-5\ge9 \Longrightarrow x\le-2\ or\ x\ge7$, using interval form $(-\infty,-2]\cup[7,\infty)$
Step 2. See graph.
