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Write the following in set-builder notation. 

The given expression represents a union of two intervals:

1. \([-4, 1]\), which includes all real numbers from \(-4\) to \(1\), inclusive.
2. \([9, \infty)\), which includes all real numbers greater than or equal to \(9\).

In set-builder notation, we describe this union of intervals as:

\[
\{ x \in \mathbb{R} \mid -4 \leq x \leq 1 \text{ or } x \geq 9 \}
\]

This notation specifies that \(x\) is a real number (\(x \in \mathbb{R}\)) and it either satisfies \(-4 \leq x \leq 1\) or \(x \geq 9\).

Would you like more details or have any further questions?

Here are 5 related questions to deepen understanding:
1. What is the difference between set-builder notation and interval notation?
2. How can the union of two sets be represented in general terms?
3. Can you explain why \([9, \infty)\) includes infinity but uses a parenthesis?
4. How do you handle inequalities when converting from interval to set-builder notation?
5. What is the impact of including or excluding boundary points in interval notation?

**Tip:** In set-builder notation, always define the set explicitly and include the type of numbers (like real numbers, integers, etc.) for clarity.

Write the following in set-builder notation.

Learn how to convert the interval notation [-4, 1] U [9, ∞) into set-builder notation. This problem covers key set theory concepts and inequalities, suitable for students in Grades 9-12.

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