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We are asked to solve the inequality \( 5|x - 2| > 10 \) and give the solution set using interval notation.

### Step-by-step solution:
1. **Isolate the absolute value**:
   \[
   |x - 2| > \frac{10}{5} = 2
   \]
   The inequality becomes:
   \[
   |x - 2| > 2
   \]

2. **Solve the absolute value inequality**:
   For \( |A| > B \), the solution is \( A > B \) or \( A < -B \).

   Therefore:
   \[
   x - 2 > 2 \quad \text{or} \quad x - 2 < -2
   \]

3. **Solve both parts**:
   - For \( x - 2 > 2 \):
     \[
     x > 4
     \]
   - For \( x - 2 < -2 \):
     \[
     x < 0
     \]

4. **Solution in interval notation**:
   The solution set is \( x > 4 \) or \( x < 0 \), which can be written in interval notation as:
   \[
   (-\infty, 0) \cup (4, \infty)
   \]

Thus, the correct choice is **A** and the solution set is \( (-\infty, 0) \cup (4, \infty) \).

---

Do you want more details or have any questions about this solution?

Here are 5 related questions you can explore:
1. How do you solve absolute value inequalities involving "less than" instead of "greater than"?
2. How would the solution change if the inequality was \( 5|x - 2| \geq 10 \)?
3. Can you explain why absolute value inequalities have two parts to solve?
4. How do we know when to use union for intervals in inequalities?
5. What happens if there is a negative coefficient in front of the absolute value?

**Tip:** When dealing with absolute value inequalities, always break it down into two separate inequalities and solve both parts.

Solve the inequality: 5|x - 2| > 10. Give the solution set using interval notation.

Learn how to solve the absolute value inequality 5|x - 2| > 10 with a step-by-step solution. The solution involves isolating the absolute value, breaking the inequality into two parts, and expressing the solution in interval notation: (-∞, 0) ∪ (4, ∞). Suitable for students in Grades 9-11.

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