To solve the inequality $|2x + 1| > 5$, we can break it down into two separate cases because of the absolute value.

Step 1: Definition of absolute value inequality

For any expression $|A| > B$, where $B > 0$, this means: $A > B \quad \text{or} \quad A < -B$ In our case, $A = 2x + 1$ and $B = 5$. Thus, the inequality becomes:

1. $2x + 1 > 5$
2. $2x + 1 < -5$

Step 2: Solve both cases

Case 1: $2x + 1 > 5$

Subtract 1 from both sides: $2x > 4$ Now, divide by 2: $x > 2$

Case 2: $2x + 1 < -5$

Subtract 1 from both sides: $2x < -6$ Now, divide by 2: $x < -3$

Step 3: Combine the solutions

The solution is: $x > 2 \quad \text{or} \quad x < -3$

In interval notation, this is: $(-\infty, -3) \cup (2, \infty)$

Would you like more details or have any questions?

---

Related Questions:

1. How do you solve absolute value inequalities where the inequality is $\leq$?
2. What is the geometric interpretation of $|x - a| > b$?
3. How do you handle inequalities with two absolute value terms?
4. What is the difference between solving $|A| > B$ and $|A| < B$?
5. Can you explain how to graph the solution set of $|2x + 1| > 5$?

Tip: Always check the boundary points when solving absolute value inequalities to ensure you don't miss any critical intervals.