Question

Graph the Inequality
1) n≤-5
二二二二一一二二一十一一一一一十>
7-6-5-4-3-2-1012345
6 7

Answer 1

To graph the inequality \( n \leq -5 \) on a number line, follow these steps:

1. **Identify the range**: The inequality means that \( n \) is less than or equal to -5. This includes -5 and all numbers less than -5.

2. **Draw the number line**: Create a horizontal line with evenly spaced numbers marked on it. Label the relevant values, including -5.

3. **Include the boundary point**: Since -5 is included in the solution (due to the "less than or equal to" symbol), you will use a closed dot (●) at -5 to indicate that this point is included in the set.

4. **Shade the region**: Shade to the left of -5, indicating that all values less than -5 are part of the solution.

Here is a textual representation of the graph:

```
<----●==================>
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5
```

In this representation:
- The circle at -5 is filled to indicate that -5 is included in the solution.
- The shading extends to the left to show all the values less than -5 are included in the solution set.