The question is asking which of the following expressions represents all real numbers except for 9.

Let's break down the options:

• A. $(- \infty, 2) \cup (2, \infty)$
  This represents all real numbers except 2, as it excludes the number 2 but includes everything else.

• B. $(- \infty, -2) \cup (-2, \infty)$
  This represents all real numbers except -2, as it excludes -2 but includes all other real numbers.

• C. $(- \infty, 9) \cup (9, \infty)$
  This represents all real numbers except 9. The union of these two intervals excludes the number 9 but includes everything else.

• D. $(- \infty, 1) \cup (1, \infty)$
  This represents all real numbers except 1, as it excludes the number 1 but includes all other real numbers.

Conclusion:

The correct option is C. $(- \infty, 9) \cup (9, \infty)$, because it represents all real numbers except 9.

Would you like more details, or do you have any further questions?

Here are five related questions:

1. What is the meaning of interval notation in set theory?
2. How do unions of intervals work in mathematics?
3. Can you represent all real numbers except for a different specific number using intervals?
4. What is the difference between open and closed intervals?
5. How would this problem change if we were excluding multiple numbers?

Tip: When using union operations on intervals, always pay attention to the endpoints to understand which numbers are included or excluded!