Graphing Linear Inequalities on a Number Line

Graphing linear inequalities on a number line is a visual way to represent all the real numbers that satisfy the inequality.

The following diagram shows how inequalities can be represented on the number line. Scroll down the page for more examples and solutions on how to graph inequalities on the number line.

 

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Key Rules for Graphing Inequalities
Open Circle (○):
Used for < (less than) or > (greater than).
The number is not included in the solution.

Closed Circle (●):
Used for ≤ (less than or equal to) or ≥ (greater than or equal to).
The number is included in the solution.

Arrow Direction:
Points to the right for > or ≥
Points to the left for < or ≤.

Graphing Inequalities on a Number Line
Graph the following inequalities on a number line<br 3x + 2 > 5
x - 5 ≤ 6
2/3 x + 4 ≥ 5
-4x + 2 ≤ 10
-x/3 + 1 > 4
2x - 8 < 0

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Solving and Graphing Linear Inequalities on a number line
3x - 4 ≤ 10
-2/3 x ≤ 2

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Solving and Graphing Linear Inequalities on a number line
7x - 4 < 3x
15 - 5(3 - 2x) ≥ 4(x - 3)

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