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The problem asks to graph the solution set for the inequality \( n \leq -4 \) or \( n \geq -5 \).

### Steps to graph the solution:

1. **Inequality 1: \( n \leq -4 \)**: 
   - This means that \( n \) includes all values less than or equal to \( -4 \). On a number line, this will be represented by a closed circle at \( -4 \) (since \( \leq \) includes \( -4 \)) and shading all values to the left.

2. **Inequality 2: \( n \geq -5 \)**:
   - This means that \( n \) includes all values greater than or equal to \( -5 \). On a number line, this will be represented by a closed circle at \( -5 \) and shading all values to the right.

### Combined Solution (Union of two inequalities):
Since this is an "or" inequality, we graph both regions:

- Shade everything from \( n = -5 \) and to the right (including all values greater than or equal to \( -5 \)).
- Shade everything from \( n = -4 \) and to the left (including all values less than or equal to \( -4 \)).

On the number line:
- The region from \( -\infty \) to \( -4 \) is shaded.
- The region from \( -5 \) to \( +\infty \) is shaded.

Since these regions overlap at \( n = -4 \) and \( n = -5 \), the entire number line will be shaded.

Would you like a detailed explanation of any part of this solution? Here are some related questions:

1. What is the difference between "and" and "or" inequalities?
2. How do you graph "and" inequalities compared to "or" inequalities?
3. What happens when inequalities overlap in their solution sets?
4. How would the solution change if this was a "strict" inequality (without the equals sign)?
5. Could this type of inequality be represented in interval notation?

**Tip:** For "or" inequalities, you always shade all regions that satisfy either inequality, unlike "and" inequalities where the shaded region is only where both are true.

Graph the solution set for n ≤ -4 or n ≥ -5.

Learn how to graph the solution set for the inequality n ≤ -4 or n ≥ -5. This covers key concepts in graphing inequalities on a number line, focusing on union of inequalities. Suitable for students in Grades 7-9.

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