Answer
$[-7, \frac{13}{2})$; see graph.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/4a08b2c9-ccb8-4a44-b1a4-46db08e5af88/result_image/1580692197.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T002129Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=479db3aee4ae9e8617a512253414d21ec93e83d8bfb078118c2140b0a6b1f310)
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.