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).