Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
Simplify the following union and or/intersection.
![The image contains the mathematical expression representing two intervals and their union:
\[
(-14, 1] \cup [-6, \infty)
\]
**Explanation:**
- **Interval (-14, 1]:** This is an interval of real numbers that starts from just greater than -14 (but not including -14) and goes up to and includes 1. The round parenthesis denotes that -14 is not included, while the square bracket indicates that 1 is included.
- **Interval [-6, ∞):** This interval starts from -6, including -6, and extends to positive infinity. The square bracket includes -6, and the round parenthesis indicates that infinity is not included, as infinity is not a finite number.
- **Union Symbol ( ∪ ):** The symbol \(\cup\) denotes the union of the two intervals, meaning the set of all numbers that belong to either one or both of the intervals.
These intervals together cover all numbers greater than -14 but not between 1 and -6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ea37998-1c84-42d7-b5a7-416d3ab84958%2F30ddd643-cf38-4957-9def-f8fb15ad17f2%2Fjmho31r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains the mathematical expression representing two intervals and their union:
\[
(-14, 1] \cup [-6, \infty)
\]
**Explanation:**
- **Interval (-14, 1]:** This is an interval of real numbers that starts from just greater than -14 (but not including -14) and goes up to and includes 1. The round parenthesis denotes that -14 is not included, while the square bracket indicates that 1 is included.
- **Interval [-6, ∞):** This interval starts from -6, including -6, and extends to positive infinity. The square bracket includes -6, and the round parenthesis indicates that infinity is not included, as infinity is not a finite number.
- **Union Symbol ( ∪ ):** The symbol \(\cup\) denotes the union of the two intervals, meaning the set of all numbers that belong to either one or both of the intervals.
These intervals together cover all numbers greater than -14 but not between 1 and -6.
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