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Let's solve the inequality \(|x + 1| > 2\).

### Step 1: Break down the absolute value inequality
The expression \(|x + 1| > 2\) can be rewritten as two separate inequalities:
1. \(x + 1 > 2\)
2. \(x + 1 < -2\)

### Step 2: Solve the two inequalities
1. \(x + 1 > 2\)
   - Subtract 1 from both sides: \(x > 1\)

2. \(x + 1 < -2\)
   - Subtract 1 from both sides: \(x < -3\)

### Step 3: Combine the results
The solution is \(x > 1\) or \(x < -3\). This is a disjunction (union), so the solution includes values where either \(x > 1\) or \(x < -3\).

### Step 4: Identify the correct graph and solution
Looking at the provided options:

- **Option B**: "Solution: \(x < -3\) or \(x > 1\)" correctly matches the solution from our work. The graph in Option B shows open circles at \(x = -3\) and \(x = 1\), with arrows extending to the left for \(x < -3\) and to the right for \(x > 1\), which is correct.

Thus, **the correct answer is Option B**.

Do you need further details or have any other questions?

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### Related Questions:
1. How do you solve inequalities involving absolute values?
2. What are the rules for solving compound inequalities?
3. How do you graph inequalities on a number line?
4. What is the difference between "and" and "or" in compound inequalities?
5. How does an absolute value inequality differ from a regular inequality?

### Tip:
When solving absolute value inequalities, always split them into two cases—one for the positive scenario and one for the negative scenario.

Solve the inequality for x and identify the graph of its solution: |x + 1| > 2

Learn how to solve the absolute value inequality |x + 1| > 2 and understand the correct graph for the solution. The solution involves separating the inequality into two cases: x > 1 or x < -3. Suitable for students in Grades 8-10.

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