The given interval is $(- \infty, -1) \cup [2, \infty)$.

We need to find an inequality that represents this union of intervals. Let's break it down:

1. $(- \infty, -1)$ represents all numbers less than $-1$.
2. $[2, \infty)$ represents all numbers greater than or equal to $2$.

Thus, the solution to this interval is:

• Either $x < -1$, meaning $x$ belongs to the first interval,
• Or $x \geq 2$, meaning $x$ belongs to the second interval.

This inequality is represented by option (a): $x < -1 \text{ or } x \geq 2$.

The other options:

• (b) does not match the intervals properly, as it describes $-1 < x \leq 2$, which is incorrect.
• (c) suggests all real numbers except $-1$ and $2$, which is incorrect because we are not excluding specific points; we are dealing with intervals.
• (d) requires $x \geq -1$ and $x \neq 2$, which is incorrect since the lower bound should be strictly less than $-1$, not including it.

Would you like further details on how these intervals are constructed or analyzed?

Here are 5 related questions to consider:

1. What is the difference between open and closed intervals in set notation?
2. How do we graphically represent union of intervals on a number line?
3. What are the key rules for solving compound inequalities involving unions?
4. How does interval notation relate to set notation?
5. How can we apply inequalities to real-world problems like budgeting or physical constraints?

Tip: When solving inequalities involving unions, always think of each interval separately before combining them!