To solve the expression \( 15 - 4 \cdot \lvert -3 - 7 \rvert \), let's break it down step by step:

1. **Calculate the expression inside the absolute value**:
   \[
   -3 - 7 = -10
   \]

2. **Take the absolute value**:
   \[
   \lvert -10 \rvert = 10
   \]

3. **Multiply by 4**:
   \[
   4 \cdot 10 = 40
   \]

4. **Subtract from 15**:
   \[
   15 - 40 = -25
   \]

So, the final answer is \(-25\).

Would you like details or have any questions about the steps? 

Here are some related questions:
1. How do absolute values affect subtraction inside them?
2. What is the difference between \(|x|\) and \(-x\)?
3. How do we simplify expressions with multiple operations and absolute values?
4. Can the absolute value of a number ever be negative?
5. What happens if we have variables inside the absolute value?

**Tip:** Always handle operations inside the absolute value before applying the absolute value itself.

Learn how to solve the expression 15 - 4 * | -3 - 7 | step-by-step with detailed explanations. This problem covers arithmetic operations and absolute value concepts. Suitable for students in Grades 7-9.

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