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The problem is asking to solve the absolute value inequality:

\[
|3x - 8| < 10
\]

### Steps to solve this:

1. **Understand the structure of the inequality**: The absolute value inequality \( |A| < B \) means that \( -B < A < B \).
   
   For \( |3x - 8| < 10 \), this translates to:
   \[
   -10 < 3x - 8 < 10
   \]

2. **Solve the inequality**:
   
   First, add 8 to all parts of the inequality:
   \[
   -10 + 8 < 3x < 10 + 8
   \]
   Simplifying:
   \[
   -2 < 3x < 18
   \]

   Now, divide all parts by 3:
   \[
   \frac{-2}{3} < x < \frac{18}{3}
   \]
   Simplifying further:
   \[
   -\frac{2}{3} < x < 6
   \]

3. **Write the solution in interval notation**:
   The solution is:
   \[
   \left( -\frac{2}{3}, 6 \right)
   \]

Thus, the answer in interval notation is \( \left( -\frac{2}{3}, 6 \right) \).

Would you like more details or have any questions?

### Related questions:
1. How do you solve absolute value inequalities with a greater-than symbol?
2. What happens when an absolute value inequality has no solution?
3. Can an absolute value inequality result in a solution with union intervals?
4. How do you graph the solution to \( |3x - 8| < 10 \) on a number line?
5. What are the differences between solving absolute value equations and inequalities?

#### Tip: 
When dealing with absolute value inequalities, always break the inequality into two cases, one for the positive and one for the negative scenario.

Solve the following inequality: |3x - 8| < 10

Explore how to solve the absolute value inequality |3x - 8| < 10 with a detailed breakdown. This page provides insights into algebraic concepts such as inequalities and absolute value, guiding you step-by-step through the problem-solving process. Suitable for high school students learning algebra.

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