Final answer:
Closed and open circles are used in mathematics to represent whether a value is included or excluded from a solution. A closed circle is filled in and represents inclusion, while an open circle is empty and represents exclusion.
Step-by-step explanation:
Closed and open circles are terms used in mathematics to describe the boundaries of a graph or equation. A closed circle is represented by a filled-in point on a number line or graph and represents that the value is included in the solution. An open circle, on the other hand, is represented by an empty point and indicates that the value is not included in the solution.
For example, in the inequality x < 5, the number 5 is not included in the solution, so an open circle would be used. In the inequality x ≤ 5, the number 5 is included in the solution, so a closed circle would be used.
Understanding closed versus open circles is important for correctly representing the solutions to equations and inequalities.