1. The problem asks to write a compound inequality describing the graph shown on the number line from 675 to 680. 2. The graph has a solid dot at 677, meaning $x \leq 677$ is included. 3. The graph has an open circle at 678, meaning $x > 678$ but not including 678. 4. The arrow extends left from 677, so all values less than or equal to 677 are included. 5. The arrow extends right from 678, so all values greater than 678 (up to 680) are included. 6. Combining these, the compound inequality is: $$x \leq 677 \text{ or } x > 678$$ This means $x$ is either less than or equal to 677, or greater than 678. Final answer: $x \leq 677 \text{ or } x > 678$