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The compound inequality given is:

\[
x \geq 40 \quad \text{and} \quad x < 45
\]

This represents the values of \( x \) that lie between 40 and 45, inclusive of 40 but exclusive of 45. To graph this on a number line:

1. **Starting at 40**, place a **closed circle** at 40 to indicate that \( x = 40 \) is included in the solution set.
2. **Ending at 45**, place an **open circle** at 45 to indicate that \( x = 45 \) is not included in the solution set.
3. Shade the line between 40 and 45 to show that all numbers between these points are included in the solution.

On the provided number line:
- Place a **closed circle** at 40.
- Place an **open circle** at 45.
- Shade the line segment between 40 and 45.

Would you like more details or further clarifications?

Here are 5 questions to deepen your understanding:
1. What does it mean when a circle is open or closed in an inequality graph?
2. How would you modify the graph if the inequality was \( x > 40 \) instead of \( x \geq 40 \)?
3. How do you graph inequalities on a two-dimensional plane?
4. How can compound inequalities be solved algebraically?
5. How does a compound inequality differ from a simple inequality?

**Tip**: Always check whether the inequality includes the endpoint to determine if it should be open (excluded) or closed (included).

Graph the compound inequality: x ≥ 40 and x < 45

Learn how to graph the compound inequality x ≥ 40 and x < 45 on a number line. This problem involves placing a closed circle at 40 and an open circle at 45, shading the area between these points to represent all values between 40 and 45.

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