The inequality you're given is:

\[
|x + 4| < 9
\]

To solve this, we break it down into two separate inequalities since the absolute value \( |A| < B \) can be rewritten as:

\[
- B < A < B
\]

In this case, \( A = x + 4 \) and \( B = 9 \). Therefore, we can write:

\[
-9 < x + 4 < 9
\]

Now, solve for \( x \) by subtracting 4 from all parts of the inequality:

\[
-9 - 4 < x < 9 - 4
\]

\[
-13 < x < 5
\]

So, the solution to the inequality is:

\[
x \in (-13, 5)
\]

### Would you like more details or have any questions?

Here are five related questions that expand on this concept:
1. How would the solution change if the inequality were \( |x + 4| \leq 9 \)?
2. What if the inequality was \( |x - 4| < 9 \)?
3. How do you solve \( |x + 4| > 9 \)?
4. What is the geometric interpretation of the inequality \( |x + 4| < 9 \)?
5. How would you solve \( |2x + 4| < 9 \)?

**Tip**: Remember, absolute value inequalities can be split into two cases, which helps solve them easily!

Learn how to solve the absolute value inequality |x + 4| < 9 with a step-by-step solution. This problem involves core algebraic concepts, such as absolute value inequalities and linear inequalities. Suitable for students in Grades 8-10.

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