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The question is asking to determine whether each set is written in interval notation or set-builder notation.

Here's the breakdown for each:

1. **[-4, 5]**: This is **interval notation**. It describes all numbers between -4 and 5, including -4 and 5 (since the brackets are closed).
   
2. **(0, 5)**: This is also **interval notation**. It describes all numbers between 0 and 5, but not including 0 or 5 (since the parentheses are open).

3. **(7, 1)**: This seems incorrect because in interval notation, the lower bound should be listed first. Normally it would be written as (1, 7). However, based on the format, this is still **interval notation**.

4. **{x | x ≥ -7}**: This is **set-builder notation**. It describes the set of all numbers \( x \) such that \( x \) is greater than or equal to -7.

5. **{x | x ≠ 3}**: This is **set-builder notation**. It describes the set of all numbers \( x \) such that \( x \) is not equal to 3.

Do you want any more details or explanations? Here are some follow-up questions to consider:

1. What is the difference between interval notation and set-builder notation?
2. How would you write the interval \( (-\infty, 3) \) in set-builder notation?
3. Can interval notation describe an unbounded set, like \( x > 7 \)? If so, how?
4. What are the implications of using open vs. closed brackets in interval notation?
5. How could you rewrite \( {x | x ≠ 3} \) in interval notation?

**Tip:** Always pay attention to whether parentheses or brackets are used in interval notation, as they define whether endpoints are included or excluded.

Decide if each set is written in interval notation or set-builder notation. Given sets: [-4, 5], (0, 5), (7, 1), {x | x ≥ -7}, {x | x ≠ 3}.

Learn how to differentiate between interval notation and set-builder notation with examples such as [-4, 5], (0, 5), (7, 1), {x | x ≥ -7}, and {x | x ≠ 3}. This topic covers key set theory concepts and is suitable for high school students.

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