Solving Inequalities in One Variable

Are you ready to dive into our inequalities unit? Let's do a very quick review of inequality basics that you probably first started learning about in second grade!

The unique thing about inequalities is that there is not just one solution, but there are multiple solutions! Think about the following inequality:

x < 5 (Read as x is less than 5) We could replace x with 4 because 4 is less than 5. We could replace x with 2 because 2 is less than 5. We could even replace x with -3 because -3 is less than 5. We could go on forever, so as you can see there are many many solutions to this inequality!

Let's take a look at the inequality symbols and their meanings again.

When you graph inequalities that have only one variable, we use a number line. We will use open and closed circles and arrows pointing to the left or right to graph our answers. Take a look at the model below.





Ok... enough review. Let's solve a few inequalities! You are going to solve inequalites, exactly the same as you solved equations. Click here if you need a refresher on solving equations.

There is however, one small rule that you always have to remember when solving inequalities! (Yes... it's always something, isn't it?) We'll get to that in a minute. Let's look at a simple inequality first!

Example 1

The next example is similar to example 1, but I would like to show you how to reverse your answer to make it easier to read and graph! Don't be afraid to do this if your variable ends up the right hand side of the inequality!

Example 2

I knew you were going to ask "Why?" And.... you should be asking why! It's important to understand these rules! Sometimes, the best explanations are through examples. Let's take a look.

This works with any true statement as long as you multiply or divide by a negative number! Go ahead, try another one! Write a true statement, and then divide by -2!






Ok... let's look at a few examples!


Our next example revists how to solve equations and/or inequalities with variables on both sides!

Example 3

Example 4

Now are you ready for a few on your own?

Click here to move onto Solving Inequalities Practice Problems.