To represent the situation where all real numbers are at least \(-8\) and at most \(0\), you would write the compound inequality as:
\[ -8 \leq x \leq 0 \]
Explanation:
- The symbol \(\leq\) indicates "at least" (or "equal to"), which means \(x\) can be equal to \(-8\).
- The upper bound of the inequality \(\leq 0\) indicates that \(x\) can also be equal to \(0\).
Graphing the Solution:
To graph this compound inequality on a number line:
- Draw a horizontal line and mark points for \( -8 \) and \( 0 \).
- Use a solid dot (or filled circle) to indicate that the endpoints \(-8\) and \(0\) are included in the solution set.
- Shade the region between \(-8\) and \(0\) to indicate all the numbers that satisfy the inequality.
Here’s how it looks visually:
<--|----|----|----------------------------------|----|----|-->
-10 -9 -8 0 1 2
●----------------●
- The solid dots at \(-8\) and \(0\) indicate that these endpoints are included.
- The shading between these points represents all the real numbers that satisfy \(-8 \leq x \leq 0\).