Solving and Graphing Inequalities

If you are beginning your study of inequalities, I have a lot of lessons for you to study. As you check them out below, make sure you start right here on this page for a quick introduction to basic inequalities.

So... what is an inequality? That's definitely not a term that we use everyday.

Let's break this word down, so that we really understand it. The term equality means that something is equal (=). Our previous unit on solving equations dealt with equalities. In this case, your math sentence would contain a simple equal sign.

The following math sentences are equalities. This means they are NOT inequalities

3+5 = 8

x + 2 = 10

x + y = 9

So... let's think about what the prefix in means in inequality. The prefix in means "not". So, an inequality means "not equal". Can you think of other signs in math that you've used besides an equals sign?

Yes, if something is not equal, then it is greater than (>) or less than (<).

Definition of Inequality

Inequality: Not equal

We use the following symbols to show that a math sentence is not equal:

<       less than

>       greater than

>       greater than or equal to 

<       less than or equal to 

Let's take a look at a few examples of simple inequality math sentences.

Inequality Math Sentences

2 < 3           Read as: 2 is less than 3

x > 8           Read as: x is greater than 8

y > 8           Read as: y is greater than or equal to 8

z < -12         Read as: z is less than or equal to negative 12

3 < x < 15    Read as: 3 is less than x and x is less than 15

This is just the beginning. There's so much to learn when studying inequalities. I've broken it down into simple, easy to understand lessons.

Make sure you take a look at all of the inequality lessons (above) that you can find on For most lessons, you'll even find an extra set of practice problems so that you can try a few on your own.

  1. Algebra
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  3. Inequalities


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