Question
One line graph open dot on -3 going left and another open dot on 3 going right
What is the solution set
What is the solution set
Answers
Answer
Options
x<-3or x>3
x<-3 and x>3
x<-3or x>3
x<-3 and x>3
Answered by
GPT-4o mini
Based on your description, it sounds like you have a graph with two open dots: one at \(-3\) and one at \(3\). Open dots typically indicate that these values are not included in the solution set.
If we're interpreting this correctly, the solution set would consist of all real numbers except for the points \(-3\) and \(3\). Therefore, the solution set can be expressed in interval notation as:
\[
(-\infty, -3) \cup (-3, 3) \cup (3, \infty)
\]
This indicates all numbers less than \(-3\), all numbers between \(-3\) and \(3\) (not including \(-3\) and \(3\)), and all numbers greater than \(3\).
If we're interpreting this correctly, the solution set would consist of all real numbers except for the points \(-3\) and \(3\). Therefore, the solution set can be expressed in interval notation as:
\[
(-\infty, -3) \cup (-3, 3) \cup (3, \infty)
\]
This indicates all numbers less than \(-3\), all numbers between \(-3\) and \(3\) (not including \(-3\) and \(3\)), and all numbers greater than \(3\).
Answered by
GPT-4o mini
Based on the options you've provided regarding the open dots at \(-3\) and \(3\):
1. **\(x < -3 \text{ or } x > 3\)**: This option correctly indicates that \(x\) can be any value less than \(-3\) or any value greater than \(3\). Since the dots are open, \(-3\) and \(3\) are not included in the solution set.
2. **\(x < -3 \text{ and } x > 3\)**: This option is incorrect because it implies that \(x\) must satisfy both conditions simultaneously, which is impossible (no number can be less than \(-3\) and greater than \(3\) at the same time).
Therefore, the correct answer is:
**\(x < -3 \text{ or } x > 3\)**.
1. **\(x < -3 \text{ or } x > 3\)**: This option correctly indicates that \(x\) can be any value less than \(-3\) or any value greater than \(3\). Since the dots are open, \(-3\) and \(3\) are not included in the solution set.
2. **\(x < -3 \text{ and } x > 3\)**: This option is incorrect because it implies that \(x\) must satisfy both conditions simultaneously, which is impossible (no number can be less than \(-3\) and greater than \(3\) at the same time).
Therefore, the correct answer is:
**\(x < -3 \text{ or } x > 3\)**.