Answer
$(-\infty,-5]\cup[2,\infty)$
See graph.
Work Step by Step
Step 1. Remove the absolute value sign to get $|2x+3|-4\ge3 \Longrightarrow |2x+3|\ge7 \Longrightarrow 2x+3\le-7\ or\ 2x+3\ge7 \Longrightarrow x\le-5\ or\ x\ge2$, and in interval form $(-\infty,-5]\cup[2,\infty)$
Step 2. See graph.
