OSEI - Inequalities Lesson

Inequalities

Inequality is a statement that two quantities are not equal. Inequalities may contain a variable.

Some examples of inequalities:

• x > 3      
• 2y ≤ 8        
• x + 5 > 4        
• y - 12 ≥ 4

Graphing the Inequality Solution

After you get a solution, you'll be asked to graph the solution. We will graph the solutions on a number line.

• If the inequality is < or >, you'll use an open circle to mark the number portion of the inequality.
• If it is ≤ or ≥ then you'll use a closed circle.

Values of the variable that make the inequality true are solutions to the inequality. A number line can be used to show the solutions to an inequality. The number line below shows the inequality x < 4.

Recall the basics in the table below:

Symbol	Meaning	Example	Read As
<	Less than	x < 5	x is less than 5
< could also be typed as <=	Less than or equal to	x < 5 could also be typed as  x<=5	x is less than or equal to 5
>	Greater than	x > 5	x is greater than 5
> could also be typed as >=	Greater than or equal to	x > 5 could also be typed as x >= 5	x is greater than or equal to 5

Solving one-variable inequalities is very much the same as solving one-variable equations. You'll still be using your opposite operations to solve the inequality.

The same properties that are used to solve equations are used to solve inequalities.

Watch the video below to learn more about solving inequalities.

Writing Inequalities

We will also be solving word problems with inequality equations. When converting words to inequalities, there are some commonly used phrases that you need to memorize and become familiar with.  

See the chart below:

Phrase	Symbol Used	Example	Inequality
Fewer than	<	Fewer than ten students studied for the exam. Let s equal the number of students that studied.	s < 10
No more than	<	The cost of c was no more than twenty.	c < 20
At most	<	The time t to take an exam should take at most fifty minutes.	t < 50
Not less than	>	In order to pass an exam, she must make not less than a 70.	g > 70
At least	>	To get an "A", the percent p must be at least a ninety.	p > 90

Steps to Writing an Inequality

Please take down important notes, such as formulas, and attempt the practice examples on your own before viewing the solutions!

Writing Inequalities

1. Write down the variable.

2. Write down the inequality symbol based on the key words used in the sentence.
3. Write down the number in the sentence.

Inequalities Assignment

Download the "Inequalities Assignment" by clicking here. Be sure to work all of the problems on paper. You will use these problems and solutions to complete the "One-Step Equations and Inequalities Homework Quiz 2." Remember you can always go back and review the lessons and videos for more help. Links to an external site.

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