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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!

Solve the inequality |x + 2| < 2 and identify the graph of its solution.

Learn how to solve the absolute value inequality |x + 2| < 2 and correctly identify its graph. This detailed solution covers absolute value concepts, solving compound inequalities, and graphing solutions on number lines. Suitable for students in Grades 8-10.

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