Question
Use interval notation and \( \cup \) to express the following: The set of all numbers less than or equal to -3 or greater than or equal to -2 .
Ask by Wilson Barnett. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The set is expressed as \((-\infty, -3] \cup [-2, \infty)\).
Solution
The set of all numbers less than or equal to \(-3\) or greater than or equal to \(-2\) can be expressed in interval notation using the union symbol \( \cup \) as follows:
\[
(-\infty, -3] \cup [-2, \infty)
\]
**Explanation:**
- \((-\infty, -3]\) represents all real numbers less than or equal to \(-3\).
- \([-2, \infty)\) represents all real numbers greater than or equal to \(-2\).
- The union \( \cup \) combines these two intervals, indicating that a number can belong to either interval to satisfy the condition.
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Simplify this solution Beyond the Answer
To express the set of all numbers less than or equal to -3 or greater than or equal to -2 in interval notation, you start with the intervals: the first part is for numbers less than or equal to -3, which is written as \( (-\infty, -3] \), and the second part is for numbers greater than or equal to -2, written as \( [-2, \infty) \). Putting these together using the union symbol, the final expression is: \[ (-\infty, -3] \cup [-2, \infty) \]
