Answer
$[-7, \frac{13}{2})$; see graph.
Work Step by Step
Step 1. From $-3\leq\frac{2x+5}{3}\lt6$, we have $-9\leq 2x+5\lt18$, $-14\leq 2x\lt13$; thus $-7\leq x\lt \frac{13}{2}$, or in interval notation $[-7, \frac{13}{2})$
Step 2. Graph the above result on a number line as shown in the figure.
