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The problem asks to graph the compound inequality:

\[
x \geq -4 \quad \text{and} \quad x < -1
\]

### Steps to graph the inequality:
1. The inequality \(x \geq -4\) means that \(x\) includes -4 and all values greater than -4. This is represented by a **closed circle** at \(x = -4\) and a line extending to the right (greater values).
2. The inequality \(x < -1\) means that \(x\) includes all values less than -1, but not -1 itself. This is represented by an **open circle** at \(x = -1\) and a line extending to the left (less than -1).

### Graph Description:
- Place a **closed circle** at \(x = -4\).
- Place an **open circle** at \(x = -1\).
- Shade the line between \(x = -4\) and \(x = -1\).

This graph represents all the values of \(x\) between \(-4\) and \(-1\), including \(-4\) but not \(-1\).

Would you like further details on inequalities or graphing? Here are five related questions:

1. What is the difference between a closed and open circle in inequality graphs?
2. How do you solve compound inequalities with "and" versus "or"?
3. Can a compound inequality have overlapping solution sets?
4. What happens if an inequality involves absolute values?
5. How do you graph compound inequalities on a number line?

**Tip:** Always pay attention to whether inequalities include the endpoints (use closed circles) or exclude them (use open circles).

Graph the compound inequality: x ≥ -4 and x < -1

This page provides a solution to graphing the compound inequality x ≥ -4 and x < -1. Learn how to represent inequalities on a number line with open and closed circles to show included or excluded values. Suitable for middle school students in Grades 6-8.

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