The given expression represents an interval for \( x \), which is the union of two disjoint intervals:

- \( x \in (-\infty, -1) \) means that \( x \) can take any value less than \(-1\).
- \( x \in (3, \infty) \) means that \( x \) can take any value greater than \( 3 \).

The symbol \( \cup \) denotes the union of these two intervals, meaning \( x \) belongs to either one of them but not the regions in between or including \(-1\) and \( 3 \).

In interval notation:
\[
x \in (-\infty, -1) \cup (3, \infty)
\]

This excludes the values \( x = -1 \) and \( x = 3 \).

Would you like more details on interval notation or its application? Here are 5 related questions:

1. How would you express \( x \in (-2, 5] \cup [7, 10) \) in words?
2. What is the difference between open and closed intervals?
3. How can you represent inequalities using interval notation?
4. How do you graph the interval \( (-\infty, -1) \cup (3, \infty) \) on a number line?
5. How do unions of intervals affect solutions in inequality problems?

**Tip**: When dealing with unions of intervals, visualize them on a number line to better understand the range of possible values.

Understand how to express and interpret the interval notation x ∈ (-∞, -1) ∪ (3, ∞), covering set theory and inequalities. This problem helps students visualize intervals on a number line, excluding boundary points. Ideal for students in Grades 9-11.

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