Question
Explain the difference between and open and closed circle when graphing an inequality.
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GPT-4o mini
When graphing inequalities on a number line, open and closed circles represent different types of inequalities:
1. **Open Circle**: An open circle is used to indicate that a value is not included in the solution of the inequality. This is typically used for inequalities with "less than" (<) or "greater than" (>) symbols. For example, if you are graphing the inequality \(x < 3\), you would place an open circle at 3 on the number line, indicating that 3 itself is not part of the solution set (the solution includes all numbers less than 3, but not 3).
2. **Closed Circle**: A closed circle indicates that a value is included in the solution of the inequality. This is used for inequalities with "less than or equal to" (≤) or "greater than or equal to" (≥) symbols. For example, for the inequality \(x \leq 3\), you would place a closed circle at 3, showing that 3 is included in the solution set (the solution includes all numbers less than or equal to 3).
In summary:
- **Open Circle**: Value is not included (used for < or >).
- **Closed Circle**: Value is included (used for ≤ or ≥).
1. **Open Circle**: An open circle is used to indicate that a value is not included in the solution of the inequality. This is typically used for inequalities with "less than" (<) or "greater than" (>) symbols. For example, if you are graphing the inequality \(x < 3\), you would place an open circle at 3 on the number line, indicating that 3 itself is not part of the solution set (the solution includes all numbers less than 3, but not 3).
2. **Closed Circle**: A closed circle indicates that a value is included in the solution of the inequality. This is used for inequalities with "less than or equal to" (≤) or "greater than or equal to" (≥) symbols. For example, for the inequality \(x \leq 3\), you would place a closed circle at 3, showing that 3 is included in the solution set (the solution includes all numbers less than or equal to 3).
In summary:
- **Open Circle**: Value is not included (used for < or >).
- **Closed Circle**: Value is included (used for ≤ or ≥).
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