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Let's analyze the mathematical problem shown in your image.

### Problem Breakdown:

1. **Sets Definition:**
   - Set \( A = \{x | x > 4\} \)
   - Set \( B = \{x | x < 2\} \)

2. **Part (a) - Union \( A \cup B \) and Graphing:**
   - The union of two sets, \( A \cup B \), consists of all elements that are in \( A \) or \( B \). In this case:
     - \( A = (4, \infty) \)
     - \( B = (-\infty, 2) \)
   - Therefore, the union is:
     \[
     A \cup B = (-\infty, 2) \cup (4, \infty)
     \]
   - You would graph this by shading the number line from \( -\infty \) to 2 (excluding 2) and from 4 to \( \infty \) (excluding 4).

3. **Part (b) - Expressing the Result with Intervals:**
   - As discussed, the result should be written using the least number of intervals, which is:
     \[
     (-\infty, 2) \cup (4, \infty)
     \]

This is the union of two disjoint intervals. To express it using the symbols provided:
- The first interval is \( (-\infty, 2) \).
- The second interval is \( (4, \infty) \).
- The union of these two is represented as:
  \[
  (-\infty, 2) \cup (4, \infty)
  \]

### Graphical Representation on the Number Line:
- The open interval \( (-\infty, 2) \) will have a shaded line from the left end extending to just before 2 (open circle at 2).
- The open interval \( (4, \infty) \) will start just after 4 (open circle at 4) and extend to the right.

Would you like more details or assistance with the graph?

Here are some related questions:
1. What is the intersection \( A \cap B \) of these two sets?
2. How would the graph differ if \( A \) and \( B \) were closed intervals instead of open?
3. Can you combine intervals when they overlap? If so, how?
4. How do you represent the complement of \( A \cup B \) on the number line?
5. What happens if you take the complement of each set separately?

**Tip:** When working with interval notation, pay close attention to open and closed brackets to correctly represent whether the endpoints are included.

Find A ∪ B if A = {x | x > 4} and B = {x | x < 2}. Then graph the resulting set and express it using intervals.

Learn how to find the union of two sets, A = {x | x > 4} and B = {x | x < 2}, and graph the result on a number line. This problem covers set theory, union of sets, and interval notation, and is suitable for high school students in grades 9-12.

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