Graphing inequalities on a number line
Choose an inequality such as x > 2, see its solutions shaded on a number line, and test numbers to find out whether they are solutions. Learn when the circle is open and when it is filled.
Core concept
An inequality such as x > 2 has many solutions, shown on a number line by a shaded arrow; an open circle means the boundary is not included (> or <), and a filled circle means it is (≥ or ≤)
Topic: Equation, inequality and graph
An equation such as x + 3 = 5 has one solution, x = 2. An inequality has many. x > 2 means “x is greater than 2”: 3, 4, 5 and 2.5 are all solutions, but 2 is not. x ≥ 2 means “greater than or equal to 2”, so 2 is a solution too. We show the solutions on a number line: a circle at the boundary, and an arrow shaded in the direction of the solutions. The circle is open (empty) for > and <, because the boundary is not included, and filled for ≥ and ≤, because it is. A number is a solution if putting it in place of x makes the inequality true.
What you will learn
- Read and write the signs >, ≥, < and ≤.
- Show an inequality on a number line with an open or a filled circle.
- Test whether a number is a solution of an inequality.
Before you start
- Know how to compare integers on a number line.
Materials
- A number line drawn on paper
Equipment
- Coloured pencils
Procedure
- With x > 2, test 3 and test 2.
- Change to x ≥ 2 and test 2.
- Show x < −1 and test a number that is a solution.
How this simulation is simplified
- The number line shows −5 to 8; the test numbers are integers.