How to Graph Inequalities on a Number Line

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By John Gugie
eHow Contributing Writer

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Number line

Graphing inequalities on number lines is done to represent the solution to inequalities with a visual representation. It aids in visualizing the answer. Graphing inequalities is simple once a few simple processes are learned. Examples appear in parentheses.

Difficulty: Moderately Easy

Instructions

Things You'll Need:

Inequality equations
Paper (graphing, if possible)
Pencil

Drawing the Number Line

Step 1

Draw a straight horizontal line.
Step 2

Draw arrows on both ends of the horizontal line, pointing outward. The arrows represent infinity.
Step 3

Draw short vertical lines at equal intervals. The number of lines, or ticks, and intervals depends on the numbers being graphed.
Step 4

Write the numbers in the vicinity of the number being graphed below the horizontal line, one for each tick.

Graphing Inequalities with Equal to or Greater / Less Than

Step 1

Figure out what the inequality solution requires. (x is equal to or greater than 1)
Step 2

Draw a solid dot on the number line where the number being graphed is represented. The solid dot represents the starting point for the inequality solution and it is part of the solution.
Step 3

Draw an arrow on the number line pointing in the direction of the inequality to infinity.
Step 4

Draw a line, thicker than the horizontal line, from the dot to the arrow. This represents all of the numbers that fulfill the inequality.

Graphing Inequalities with Greater / Less Than

Step 1

Figure out what the inequality solution requires. (x is less than 1)
Step 2

Draw an open dot on the number line where the number being graphed is represented. The open dot represents the starting point for the inequality solution but is not part of the solution.
Step 3

Draw an arrow on the number line pointing in the direction of the inequality to infinity.
Step 4

Draw a line, thicker than the horizontal line, from the dot to the arrow. This represents all of the numbers that fulfill the inequality.