Question
AJ solved the absolute value inequality |x|>1 . He used the "or rule," which meant that his solution would have two parts. In interval notation, the first part of the solution AJ found was (−∞,−1) . Find the second part of the solution.(1 point) The solution to |x|>1 is (−∞,−1)∪ (
Answers
GPT-4o mini
To solve the absolute value inequality \(|x| > 1\), we interpret it as meaning that \(x\) is either greater than 1 or less than -1. Thus, we have two cases:
1. \(x > 1\)
2. \(x < -1\)
The first part of the solution provided by AJ is \((-\infty, -1)\), which corresponds to the second case.
The second part of the solution corresponds to the first case where \(x > 1\). In interval notation, this is represented as \((1, \infty)\).
Thus, the complete solution to \(|x| > 1\) in interval notation is:
\[
(-\infty, -1) \cup (1, \infty)
\]
So, the answer to your question is:
The solution to \(|x| > 1\) is \((-\infty, -1) \cup (1, \infty)\).
1. \(x > 1\)
2. \(x < -1\)
The first part of the solution provided by AJ is \((-\infty, -1)\), which corresponds to the second case.
The second part of the solution corresponds to the first case where \(x > 1\). In interval notation, this is represented as \((1, \infty)\).
Thus, the complete solution to \(|x| > 1\) in interval notation is:
\[
(-\infty, -1) \cup (1, \infty)
\]
So, the answer to your question is:
The solution to \(|x| > 1\) is \((-\infty, -1) \cup (1, \infty)\).