By Grade 5 at Think Academy (Grade 6 in school), students begin graphing one-variable linear inequalities. The most common hurdles are mixing up open vs. closed circles and knowing which direction to shade. This guide gives clear steps to avoid those mistakes and read number lines with confidence.

What Are Inequalities?

An inequality is like an equation, but instead of showing two sides are equal, it shows that one side is bigger, smaller, or possibly equal to the other.

Inequalities describe a range of possible answers, not just one solution.

What Is a Number Line?

A number line is a straight line used to show numbers in order.

It has three main parts:

1. Origin (zero): The point where we start, usually marked as 0.
2. Unit length: The distance between two marks, showing one step (for example, from 0 to 1).
3. Positive direction: Numbers increase to the right (positive), and decrease to the left (negative).

On a number line, every point stands for a number. This makes it much easier to see and understand solutions to equations and inequalities.

Five Types of Relationships on a Number Line

When we graph inequalities, we use open circles and closed circles:

Let’s see each type.

Equal to (=)

Example:

On the number line, we put a closed circle at 7, because the solution is exactly 7.

Greater than (>)

Example:

Draw an open circle at 7, and shade the line to the right. This shows that all numbers bigger than 7 work.

Less than  (<)

Example:

Draw an open circle at 7, and shade the line to the left. This shows all numbers smaller than 7 work.

Greater than or Equal to (≥)

Example:

Draw a closed circle at 7, and shade to the right. The solution includes 7 and everything bigger.

Less than or Equal to  (≤)

Example:

Draw a closed circle at 7, and shade to the left. The solution includes 7 and everything smaller.

Example Problems: Graphing One-Variable Linear Inequalities

Example 1

Graph the inequality on the number line.

???? ≥ 0

Solution:

Example 2

Graph the inequality on the number line.

???? ≤ −1

Solution:

Summary: Graphing One-Variable Linear Inequalities

Graphing one-variable linear inequalities is all about:

• Knowing the inequality/equality sign (>, <, ≥, ≤, =);
• Deciding if the circle is open or closed;
• Shading the correct side of the number line.

Want more printable practice?

Additional Math Topics for Grade 6 Linear Equations – with Free Worksheets

More Middle School Algebra Resources Ready for You

We’ve created a full library of printable resources — from foundational math to logic-based challenges — organized by grade to support every stage of your child’s journey.

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