Question

Graph the compound inequality on the number line.
x> -6 and x≤7

Answer 1

To graph the compound inequality \(x > -6\) and \(x \leq 7\) on a number line, follow these steps:

1. **Identify the critical points**: The two critical points from the inequalities are \(-6\) and \(7\).

2. **Graph the first inequality \(x > -6\)**:
- Since \(x > -6\) is an open interval, represent \(-6\) with an open circle (meaning \(-6\) is not included in the solution set).
- Shade to the right of \(-6\) to show that all numbers greater than \(-6\) are included.

3. **Graph the second inequality \(x \leq 7\)**:
- For \(x \leq 7\), use a closed circle at \(7\) (meaning \(7\) is included in the solution set).
- Shade to the left of \(7\) to indicate all numbers less than or equal to \(7\) are included.

4. **Combine the two graphs**:
- You will shade the region between \(-6\) (not included) and \(7\) (included).

Here's a simple representation of the number line:

```
<--|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|---->
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
(-------------]
```

**Key Points**:
- The open circle at \(-6\) indicates that \(-6\) is NOT included.
- The closed circle at \(7\) indicates that \(7\) IS included.
- The shaded area between \(-6\) and \(7\) represents the solution to the compound inequality \(x > -6\) and \(x \leq 7\).