Question
Use interval notation to express the following: The set of all numbers greater than -8 and less than 1 .
Ask by Riley Bird. in the United States
Feb 03,2025
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Answer
The set of all numbers greater than -8 and less than 1 is written as (-8, 1).
Solution
The set of all numbers greater than \(-8\) and less than \(1\) can be expressed in interval notation as:
\[
(-8, 1)
\]
**Explanation:**
- The parentheses \(( )\) indicate that \(-8\) and \(1\) are **not** included in the set (i.e., the inequalities are strict: \( -8 < x < 1 \)).
- If the endpoints were to be included, square brackets \([ ]\) would be used instead.
So, the interval \((-8, 1)\) represents all real numbers \(x\) such that \(-8 < x < 1\).
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Simplify this solution Extra Insights
The interval notation for the set of all numbers greater than -8 and less than 1 is (-8, 1). In interval notation, parentheses are used to indicate that -8 and 1 are not included in the set, meaning the values can get infinitely close to -8 and 1, but never actually include those endpoints. Remember, if you ever need to denote a number that is included in the set as well, you'd use square brackets. For example, if you were representing numbers greater than or equal to -8 and less than or equal to 1, it would be expressed as [-8, 1]. Just a handy tip when working with intervals!
