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.