To represent the situation where all real numbers are at least -6 and at most 3, you should write the compound inequality as:
\[ -6 \leq x \leq 3 \]
This indicates that \(x\) can take any value starting from -6 up to and including 3.
Graphing the Solution:
- Draw a number line.
- Place solid dots (or closed circles) at -6 and 3 to indicate that these endpoints are included in the solution set.
- Shade the region between -6 and 3 to show all the numbers that are part of the solution.
Here’s a visual representation:
<---|----|----|----|----|----|----|----|----|----|---->
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
•================•
\-6 ≤ x ≤ 3/
In this graph:
- The solid dots at -6 and 3 show that these values are included in the inequality.
- The line between them indicates all the values that \(x\) can take, fulfilling the compound inequality.