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?

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.