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The inequality presented is:

\[
|x + 4| > 3
\]

To solve this, we break it into two cases because the absolute value inequality \( |A| > B \) can be written as two inequalities:

\[
x + 4 > 3 \quad \text{or} \quad x + 4 < -3
\]

### Case 1: \( x + 4 > 3 \)
Solve for \(x\):
\[
x > 3 - 4
\]
\[
x > -1
\]

### Case 2: \( x + 4 < -3 \)
Solve for \(x\):
\[
x < -3 - 4
\]
\[
x < -7
\]

Thus, the solution to the inequality is:
\[
x > -1 \quad \text{or} \quad x < -7
\]

In interval notation, this solution is:
\[
(-\infty, -7) \cup (-1, \infty)
\]

Would you like any further details or clarifications?

Here are some related questions you might find useful:
1. How do we solve absolute value inequalities where the inequality sign is \( \leq \)?
2. What is the difference between strict inequalities \( > \) and non-strict inequalities \( \geq \)?
3. Can absolute value inequalities have solutions that are all real numbers?
4. How do we graph the solution set of an absolute value inequality on a number line?
5. What happens if the inequality is \( |x + 4| = 3 \) instead of \( > 3 \)?

**Tip:** When solving absolute value inequalities, always remember to split them into two cases—positive and negative—to find all possible solutions.

Solve the absolute value inequality: |x + 4| > 3

Learn how to solve the absolute value inequality |x + 4| > 3 with a step-by-step solution. This problem focuses on absolute value inequalities and algebraic manipulation, suitable for students in Grades 9-11.

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