The problem is asking you to solve the inequality $|x + 2| < 2$ and identify the correct graph and solution.

Step 1: Solve the absolute value inequality

To solve $|x + 2| < 2$, you can rewrite it as a compound inequality without the absolute value:

$-2 < x + 2 < 2$

Step 2: Solve for $x$

Now subtract 2 from all parts of the inequality:

$-2 - 2 < x + 2 - 2 < 2 - 2$

This simplifies to:

$-4 < x < 0$

So the solution to the inequality is $x$ between $-4$ and $0$, not including $-4$ or $0$.

Step 3: Identify the correct graph

From the given options, the correct graph is the one that shows the range $-4 < x < 0$, with open circles at $-4$ and $0$ to indicate that these points are not included. This corresponds to Option D.

Final Answer:

The correct answer is D: Solution: $x > -4$ and $x < 0$.

Do you want further details or have any questions? Here are 5 related questions to think about:

1. What is the difference between strict and non-strict inequalities?
2. How would the solution change if the inequality were $|x + 2| \leq 2$?
3. How do you graph an inequality on a number line when dealing with absolute values?
4. What happens if the inequality has a "greater than" sign instead of a "less than" sign?
5. How would the solution change if we had $|x + 2| > 2$?

Tip: Always remember to check the boundaries carefully when solving absolute value inequalities!