1. The problem is to write a compound inequality based on a number line graph. 2. The graph shows a line segment from approximately -619 to -614 with an open circle at -617 and a closed circle at -616. 3. An open circle means the endpoint is not included in the inequality, so for -617, we write $x > -617$. 4. A closed circle means the endpoint is included, so for -616, we write $x \leq -616$. 5. Since the line connects these two points, the compound inequality combines these two parts. 6. Thus, the compound inequality is $$-617 < x \leq -616$$. 7. This describes all $x$ values greater than -617 but less than or equal to -616.