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The question is asking which set of numbers represents those that are either less than \(-10\) or greater than or equal to \(-8\).

Let's break down the options:

1. **\(\{x \mid x < -10 \text{ or } x > -8\}\)**: This set describes numbers that are either less than \(-10\) or greater than \(-8\). This doesn't match the given condition fully, as it excludes numbers equal to \(-8\).

2. **\(\{x \mid x < -10 \text{ and } x > -8\}\)**: This set describes numbers that are both less than \(-10\) and greater than \(-8\), which is impossible, since a number cannot satisfy both conditions at the same time. So, this is incorrect.

3. **\(\{x \mid x \leq -10 \text{ or } x \geq -8\}\)**: This set describes numbers that are either less than or equal to \(-10\) or greater than or equal to \(-8\). This seems like a valid match for the problem condition, which is looking for numbers less than \(-10\) or greater than or equal to \(-8\).

4. **\(\{x \mid x \leq -10 \text{ and } x \geq -8\}\)**: This set describes numbers that are both less than or equal to \(-10\) and greater than or equal to \(-8\), which is another impossible condition, because no number can satisfy both simultaneously.

### Correct Answer:
The correct answer is **\(\{x \mid x \leq -10 \text{ or } x \geq -8\}\)**, which matches the third option.

Would you like further details or have any questions?

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Here are five related questions for further exploration:
1. What is the difference between "and" and "or" in set notation?
2. How do you represent inequalities on a number line?
3. Can two inequalities combined with "and" ever result in an empty set?
4. What is the union of two sets in terms of inequalities?
5. How does set notation differ from interval notation?

**Tip**: Always pay close attention to the symbols used in inequalities, such as "or" (union) vs. "and" (intersection), as they drastically change the meaning of the solution set.

Which is the set of numbers less than -10 or greater than -8?

Identify the set of numbers that satisfy the condition of being less than -10 or greater than -8. Explore the use of set notation and inequalities, suitable for students in Grades 9-12. The problem demonstrates understanding of set unions and intersections.

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