Question

Write a compound inequality that represents each situation. Graph your solution.


all real numbers at least –6 and at most 3









–6 > x > 3

Answer 1

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:

1. Draw a number line.
2. Place solid dots (or closed circles) at -6 and 3 to indicate that these endpoints are included in the solution set.
3. 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.