Explain the difference between and open and closed circle when graphing an inequality.

Answer 1

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 ≥).