https://r2.erweima.ai/mathbot/image/1725971821181v4ghxoc0.jpg

The inequality provided in the image is:

\[
3|x - 10| < 15
\]

### Step-by-step solution:

1. **Divide both sides by 3** to simplify the inequality:

\[
|x - 10| < 5
\]

2. **Interpret the absolute value inequality**:
   \[
   |x - 10| < 5 \implies -5 < x - 10 < 5
   \]

3. **Solve for \(x\)** by adding 10 to all parts of the inequality:

\[
-5 + 10 < x < 5 + 10
\]

\[
5 < x < 15
\]

### Final Answer:
\[
5 < x < 15
\]

Thus, the correct solution is **5 < x < 15**, which matches the answer in the provided options. The correct option is the third choice.

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Would you like further details or clarification on this? Here are some additional related questions to consider:

1. How do you solve absolute value inequalities?
2. Can absolute value inequalities have no solutions?
3. What happens when the inequality is \( \geq \) or \( \leq \) instead of strict \( < \)?
4. How does dividing or multiplying by a negative number affect an inequality?
5. How can you graph this solution on a number line?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number.

Learn how to solve the absolute value inequality 3|x - 10| < 15 with a detailed step-by-step explanation. This problem covers key concepts such as absolute value inequalities and linear inequalities, suitable for students in Grades 9-11.

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