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Graphing single-variable inequalities

There are just a few important concepts that you must know in order to graph an inequality. Let’s review a number line.

Graphing-single-variable-inequalities-1

The negative numbers are on the left of the zero and the positive numbers are on the right.

Example 1


\(r >  - 5\)


This is read as “r is greater than -5.” This means it includes all numbers greater than, or to the right, of -5 but does not include -5 itself. We will have to show this by using an open circle and having the arrow shoot out to the right.


Graphing-single-variable-inequalities-2

Example 2


\(x \le 0.4\)

 

This is read as “x is less than or equal to 0.4.” This time we include the 0.4 by using a closed circle and the arrow will shoot out to the left. The number 0.4 is in between the 0 and the 1 on a number line.

Graphing-single-variable-inequalities-3

Example 3


\( - 3 < p\)

 

Be careful with this one! Since it is backwards, it is read as “p is greater than -3.” You always read an inequality starting with the variable. This means that the graph will have an open circle and will shoot out to the right.

Graphing-single-variable-inequalities-4

Here is a summary of the important details in graphing inequalities.

 Make sure you read the inequality starting with the variable!

 

“greater than” or “greater than or equal to”        – arrow shoots out to the right

“less than” or “less than or equal to”                 – arrow shoots out to the left

will have open circles
\( \le \) and \( \ge \) will have closed circles


Below you can download some free math worksheets and practice.


Downloads:
3334 x

Draw a graph for each inequality.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Inequalities-Graphing-single-variable-inequalities-easy

Watch below how to solve this example:

 

Downloads:
2973 x

Draw a graph for each inequality.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Inequalities-Graphing-single-variable-inequalities-medium

Watch below how to solve this example:

 

Downloads:
3140 x

Draw a graph for each inequality.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Inequalities-Graphing-single-variable-inequalities-hard

Watch below how to solve this example:

 
 
 

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