The compound inequality provided is:

$x \geq -2 \quad \text{and} \quad x \leq 1$

This can be rewritten as:

$-2 \leq x \leq 1$

Graphing the inequality:

1. The inequality $x \geq -2$ means the value at $-2$ is included (closed circle) and extends to the right.
2. The inequality $x \leq 1$ means the value at $1$ is included (closed circle) and extends to the left.

On the number line:

• Place a closed circle at $x = -2$ and another closed circle at $x = 1$.
• Draw a line connecting these two points, representing all the values between $-2$ and $1$, inclusive.

This is how the graph would look on a number line between $-2$ and $1$, with closed circles at both endpoints.

Would you like more details on solving compound inequalities?

Here are 5 related questions for further practice:

1. How would the graph change if the inequality were $x > -2$ and $x \leq 1$?
2. What is the solution to the inequality $-3 \leq x < 2$?
3. How can you solve compound inequalities involving three parts, like $-3 \leq x < 2 \leq y$?
4. What are the steps to solving and graphing $-5 < x < 0$?
5. Can you graph a compound inequality involving absolute values, like $|x| \leq 4$?

Tip: When graphing inequalities, always check if the endpoints are included (closed circles) or not (open circles).