# The Order of Real Numbers: Inequalities

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Finding the Absolute Value of a Real Number

### You're on a roll. Keep up the good work!

Replay
Your next lesson will play in 10 seconds
• 0:07 Which Is Bigger?
• 0:32 Less Than or Greater Than
• 1:15 How to Use Inequalities
• 4:03 Lesson Summary

Want to watch this again later?

Timeline
Autoplay
Autoplay
Create an account to start this course today
Try it free for 5 days!

#### Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Jennifer Beddoe
An inequality is an operation describing how one number can be compared to another. This lesson will describe and define inequalities and the symbols used to represent them. It will also give some examples on how to work with inequalities.

## Which is Bigger?

When you were little, did your teacher ever ask your class to line up from tallest to smallest? Or have you ever lined something from smallest to greatest? I know I like the spice jars in the cabinet in my house to be lined up according to size. This type of organization deals with deciding the 'unequalness' of things, which of them are bigger or which of them are smaller than all the others.

## Less Than or Greater Than

In mathematics, lining up numbers according to size involves the use of inequalities. An inequality is the relationship between two values that are different. Working with inequalities involves determining what that relationship is -- how each number is bigger or smaller than the other numbers in a particular group. The notation for inequalities consists of the following symbols:

These symbols are used to notate exactly what they say. If you have two quantities, the symbols can be used to show which one is larger or smaller than the other.

## How to Use Inequalities

Inequalities can be used in many different ways. First, they can be used to show the relationship between two quantities. For example:

1 < 13

and

7.5 > 7.2

Inequalities are a good way to show the differences between real numbers that might not be easily apparent at a glance.

Real numbers are all numbers that are not imaginary. They include the following sets of numbers:

• Whole numbers, which are non-negative numbers that are not fractions or decimals.
• Integers , which are all numbers that are not fractions or decimals, including negative numbers.
• Rational numbers are positive and negative numbers that include fractions and decimals.
• Irrational numbers include decimal numbers that cannot be written as fractions, for example: e and pi.

Here's another example:

sqrt. 2 < pi

2/3 > 0.15

The second way you can use inequalities is to solve problems, such as:

Given the inequality a < b, write another inequality with the same meaning.

Answers to this question might be things like:

2 < 6

or

1.8 > sqrt. 3

Lastly, inequalities can be used to write true or false statements, such as:

Is the statement '-5 is greater than or equal to -3' true or false?

For problems like these, if it's not easy to see the answer, it can be helpful to draw a number line to help you figure it out.

To unlock this lesson you must be a Study.com Member.

### Register for a free trial

Are you a student or a teacher?
Back

Back

### Earning College Credit

Did you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.