Question
Express the interval using two different representations. \[ [-6,-1] \]
Ask by Hamilton Blake. in the United States
Jan 20,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The interval \([-6, -1]\) can also be written as:
- **Inequality:** \(-6 \leq x \leq -1\)
- **Set-Builder Notation:** \(\{\, x \mid -6 \leq x \leq -1 \,\}\)
Solution
Certainly! The interval \([-6, -1]\) can be expressed in different forms. Here are two alternative representations:
1. **Inequality Notation:**
\[
-6 \leq x \leq -1
\]
This means that \(x\) is a number that is greater than or equal to \(-6\) and less than or equal to \(-1\).
2. **Set-Builder Notation:**
\[
\{\, x \mid -6 \leq x \leq -1 \,\}
\]
This describes the set of all real numbers \(x\) such that \(x\) satisfies the condition \(-6 \leq x \leq -1\).
These representations provide different ways to describe the same interval, useful in various mathematical contexts.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
First off, let’s put on our math hats! The interval \([-6, -1]\) can be expressed in set notation as \(\{x \,|\, -6 \leq x \leq -1\}\). This means we're talking about all the numbers \(x\) that lie between -6 and -1, inclusive! Now, let’s sprout some stylish brackets! We can also represent this interval using interval notation as \([-6, -1]\), which is the same as the original but presented with some finesse. This notation clearly indicates that both endpoints -6 and -1 are part of the interval!
