Graphing With an Empty Circle
When graphing an inequality on a number line, the type of circle used at the boundary point tells you whether that point is included in the solution. A strict inequality using > (greater than) or < (less than) uses an empty (open) circle, showing that the boundary number is NOT part of the solution. A non-strict inequality using ≥ or ≤ uses a filled (closed) circle. For example, graphing x > 3 uses an open circle at 3 with an arrow pointing right. This 7th grade math skill is covered in Saxon Math, Course 2, and is foundational for algebra.
Key Concepts
Property To graph an inequality with $ $ (greater than) or $ < $ (less than), use an empty circle to show the boundary number is not included in the solution.
Examples Graph of $x 5$: An empty circle on the number 5 with a ray shaded to the right. Graph of $x < 0$: An empty circle on the number 0 with a ray shaded to the left.
Explanation An empty circle is like a fence that you can get right up against but can't touch. For $x 4$, you can include 4.001 or $4\frac{1}{2}$, but not 4 itself. The empty circle sits right on 4 to say, 'The solutions start right after this spot!' It's the perfect way to exclude a single point.
Common Questions
What does an open circle mean on a number line?
An open (empty) circle on a number line indicates that the boundary value is NOT included in the solution. It is used with strict inequalities like > (greater than) or < (less than).
What does a closed circle mean on a number line?
A closed (filled) circle on a number line means the boundary value IS included in the solution. It is used with inequalities like ≥ (greater than or equal to) or ≤ (less than or equal to).
How do you graph an inequality on a number line?
Identify the boundary value and draw either an open or closed circle there. For ‘>’ or ‘<’ use an open circle; for ‘≥’ or ‘≤’ use a closed circle. Then shade or draw an arrow in the direction of all solutions.
What is the difference between greater than and greater than or equal to?
Greater than (>) means strictly larger than a value, so the boundary is not included (open circle). Greater than or equal to (≥) includes the boundary value itself (closed circle).
Why does the type of circle matter when graphing inequalities?
The type of circle communicates exactly which values are solutions. Using the wrong type of circle is a mathematical error — it changes whether the boundary number is a valid solution.
When do students learn to graph inequalities?
Graphing inequalities on a number line is typically introduced in 7th grade pre-algebra and continues in 8th grade algebra.
Which textbook covers graphing with an open circle?
Saxon Math, Course 2 covers how to graph inequalities with open and closed circles.