https://file.aiquickdraw.com/mathbot/file/1729187431188835qjiis.jpg

The problem asks to solve the absolute value inequality:

\[
|x - 4| < 9
\]

To solve this, we use the property of absolute value inequalities. For any inequality of the form \(|A| < B\), the equivalent inequality is:

\[
-B < A < B
\]

### Step 1: Apply the property
For the inequality \(|x - 4| < 9\), we rewrite it as:

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

### Step 2: Solve the compound inequality
Now, solve for \(x\) by adding 4 to all parts of the inequality:

\[
-9 + 4 < x < 9 + 4
\]
\[
-5 < x < 13
\]

### Final Solution:
The solution to the inequality is:

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

This means that \(x\) lies between \(-5\) and \(13\), but does not include these endpoints.

---

Would you like more details, or do you have any further questions?

Here are five related questions you might find helpful:
1. How do you solve an absolute value inequality when it's greater than a number?
2. What are the differences between strict and non-strict inequalities in absolute values?
3. How can absolute value inequalities be used in real-life applications?
4. What happens if there's a negative number on the right side of an absolute value inequality?
5. Can absolute value inequalities have no solution? If so, when?

**Tip:** Always check if you can simplify the inequality or equation before solving it. This makes solving easier and reduces errors.

Learn how to solve the absolute value inequality |x - 4| < 9. This step-by-step guide covers algebraic concepts and provides a clear solution for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation