What are the open circle and closed circle on a number line for greater than and less than

Answer 1

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 ≤)