Pengi Editor's Note: This article was originally published by Think Academy. We're sharing it here for educational value. Think Academy is a leading K-12 math education provider.
How to Graph One-Variable Linear Inequalities on a Number Line
By Grade 6, 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.
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:
- Origin (zero): The point marked as 0
- Unit length: The distance between two marks
- Positive direction: Numbers increase to the right
Five Types of Relationships on a Number Line
When graphing inequalities, we use open circles and closed circles:
Equal to (=)
Put a closed circle at the exact value — the solution is that exact number.
Greater than (>)
Draw an open circle at the value, shade to the right. (The value itself is NOT included.)
Less than (<)
Draw an open circle at the value, shade to the left. (The value itself is NOT included.)
Greater than or Equal to (≥)
Draw a closed circle at the value, shade to the right. (The value IS included.)
Less than or Equal to (≤)
Draw a closed circle at the value, shade to the left. (The value IS included.)
Example Problems
Example 1
Graph: 𝑥 ≥ 0
Solution: Draw a closed circle at 0 and shade to the right.
Example 2
Graph: 𝑥 ≤ −1
Solution: Draw a closed circle at −1 and shade to the left.
Summary
Graphing one-variable linear inequalities is all about:
- Knowing the inequality sign (>, <, ≥, ≤, =)
- Deciding if the circle is open (strict inequality) or closed (includes the value)
- Shading the correct side of the number line
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