Question
What are the open circle and closed circle on a number line for greater than and less than
Answers
GPT-4o mini
On a number line, open circles and closed circles are used to represent inequalities clearly:
1. **Open Circle**: An open circle at a point on the number line indicates that the value at that point is **not included** in the solution set. It's used for inequalities involving "greater than" (>) or "less than" (<).
- Example: For \( x > 3 \), you would place an open circle at 3, indicating that 3 is not part of the solution (solutions include numbers greater than 3).
- Example: For \( x < 2 \), you would place an open circle at 2, indicating that 2 is not part of the solution (solutions include numbers less than 2).
2. **Closed Circle**: A closed circle at a point on the number line indicates that the value at that point is **included** in the solution set. It's used for inequalities involving "greater than or equal to" (≥) or "less than or equal to" (≤).
- Example: For \( x \geq 4 \), you would place a closed circle at 4, indicating that 4 is included (solutions include 4 and all numbers greater than 4).
- Example: For \( x \leq -1 \), you would place a closed circle at -1, indicating that -1 is included (solutions include -1 and all numbers less than -1).
In summary:
- Open circle: Not included (used for > and <)
- Closed circle: Included (used for ≥ and ≤)
1. **Open Circle**: An open circle at a point on the number line indicates that the value at that point is **not included** in the solution set. It's used for inequalities involving "greater than" (>) or "less than" (<).
- Example: For \( x > 3 \), you would place an open circle at 3, indicating that 3 is not part of the solution (solutions include numbers greater than 3).
- Example: For \( x < 2 \), you would place an open circle at 2, indicating that 2 is not part of the solution (solutions include numbers less than 2).
2. **Closed Circle**: A closed circle at a point on the number line indicates that the value at that point is **included** in the solution set. It's used for inequalities involving "greater than or equal to" (≥) or "less than or equal to" (≤).
- Example: For \( x \geq 4 \), you would place a closed circle at 4, indicating that 4 is included (solutions include 4 and all numbers greater than 4).
- Example: For \( x \leq -1 \), you would place a closed circle at -1, indicating that -1 is included (solutions include -1 and all numbers less than -1).
In summary:
- Open circle: Not included (used for > and <)
- Closed circle: Included (used for ≥ and ≤)