How do you read aloud a probability notation in English?

Question

I'm learning probability and I'm trying to "translate" one line from mathematical notation to English.

It's the definition of a random variable:

$$\textbf{X}^{-1}(-\infty,x)=\{w\in\Omega;\textbf{X}(\omega)<x\}$$

Answer 1

I would read the line $$\textbf{X}^{-1}((-\infty,x)) = \{\omega \in \Omega \: | \: \textbf{X}(\omega) < x\}$$ as : "The preimage under $X$ of the open interval from minus infinity to $x$ is equal to the set of $\omega$ for which $X(\omega)$ is strictly less than $x$."

An alternative formulation could be: "The preimage under $X$ of the open interval from minus infinity to $x$ is equal to the set on which $X$ is less than $x$."