Are you ready to dive into our solving inequalities unit? Let's do a very quick review of inequality basics that you probably first learned about in second grade.
Always remember that inequalities do not have just one solution. There are always multiple solutions! Think about the following inequality:
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.
An open circle on the graph indicates less than (<) or greater than (>).
A closed circle on the graph represents less than or equal to (<) or greater than or equal to (>).
Take a look at the model below.
Ok... enough review. Let's solve a few inequalities. You are going to solve inequalites using the exact same rules that you used when solving equations. Let's quickly review those rules:
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.
Did you notice that you took the exact same steps that you would've taken in order to solve a regular equation? The only difference was that you had a less than sign instead of an equal sign.
Now that was pretty easy!
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.
Ok... The first two examples should have been pretty easy since you are a superstar at solving equations. Luckily there's only one trick that you have to remember when solving inequalities and that is:
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.
Our last example revists how to solve equations and/or inequalities with fractions. I hope you remember the trick.
Now are you ready for a few on your own?
Try entering your problem here for the answer.
Sign Up for Algebra Class E-courses
"I'd like to start off by relaying my sincerest gratitude for your dedication in teaching algebra. Your methodology is by far the simplest to follow, primarily because you take the time to include the small steps in between that most other teachers leave out.
It helps to know why you are doing something. I am 45 and heading to college to get my BS in Business. I need to brush up, hence the visit to your site. Great Job!"
Jimmy - United States
"I stumbled onto your site after I found out that I needed to use some fundamental algebra for an assignment. Turns out I had forgotten some things and your great site helped me remember them like "that" (snap of fingers). The organization of the site let me find exactly what I was looking for so easily. Kudos to you for maintaining such a great resource for students of all ages!"
Tom - United States
"I just wanted to write and basically thank you for making such a wonderful website! I'm 20 years old and about to take a basic placement test for college. I wanted to brush up on my Algebra skills and I stumbled upon your site. I'm amazed at how simple you make it and how fast I'm remembering Algebra! I don't remember getting most of the answers right when I had an actual teacher in front of me teaching this. Thanks a lot!"
Elizabeth - United States
"I am a pensioner living in South Africa. I stumbled on your website, the best thing that could ever happen to me! Your course in Algebra has helped me a lot to better understand the different concepts. Thank you very much for sharing your skills for teaching math to even people like me. Please do not stop, as I am sure that your teachings have helped thousands of people like me all over the world."
Noel - South Africa
This is an amazing program. In one weekend I used it to teach my Grade 9 daughter most of the introductory topics in Linear Relations. I took her up to Rate of Change and now she can do her homework by herself.
Reg - United States
Copyright © 2009-2013 Karin Hutchinson ALL RIGHTS RESERVED