This document provides a quick lesson on combining like terms and solving simple algebraic equations, emphasizing the importance of simplifying problems. It explains that like terms have the same variables and offers examples and visual aids to help identify and combine them effectively. The document aims to make mathematical problems more manageable by demonstrating how to simplify expressions.

1. Combining Like Terms and Solving Equations A quick lesson in simple Algebra

2. Combining Like Terms In Algebra, there is no better way to make your life easier than to learn how to simplify problems by combining like terms. Ok, well, maybe not that easy. But just think, by combining like terms, you make problems shorter and simpler. Ming Xia, “ Easy Cheese ” October 8, 2005 via Flickr, Creative Commons Attribution, Share Alike.

3. Which would you rather have This problem: Or, this one:

4. Which would you rather have This problem: Or, this one: Believe it or not, they are the same problem, but I sure would rather deal with the second one.

5. So, what is a like term? Like terms are terms that have the same variables in the same form or an equivalent form. Blah, blah, blah. The people who write math books are too smart for their own good. This just means that in like terms, the variable parts match. Powerhouse Museum Collection, “ Man [Eric Sheldon?] eating banana and reading sheet music ” uploaded September 1, 2009 via Flickr, Public Domain.

6. On to an example Simplify by adding like terms: Our first step will always be to rewrite the problem with the variables in alphabetical order.

7. Identify like terms Now, starting with the first term, go through and put a circle around all of the terms that match it. Notice how I included the sign in front of each term. This will be important later. Now, do the next term with a different shape.

8. Identify and combine like terms Etc. etc. until all terms are “identified”. Now, I can put my shapes together. I’ll start with my red circles. A 1 st Grade review: “put together” means what?

9. Combine like terms Then, do the same thing with your other shapes. Now I can rearrange my pieces to get my answer.

10. Combining Like Terms Part 2 Putting Apples with Apples and Oranges with Oranges User “Fir0002”, “ Sundown and cross section ” January 22, 2009 via Wikimedia Commons, GNU Free Documentation License 1.2 . User “Neutrality”, “ Citrus sinensis ” December 11, 2005 via Wikimedia Commons, Public Domain.

11. Simplify by Adding Like Terms Look at that mess. Wow!! Remember, we want to “simplify” to make your life easier! First we want to move the letters around so that they are in the same order in each term.

12. Now that the variables in our terms are all in order, let’s do something that may seem strange. In case you don’t like the circles and squares from before, let’s do it differently. Let’s say that every is an apple, and every is an orange. Makes sense since we are comparing apples and oranges.

13. So, now we will get a different looking problem. Now, what does that give me? Now just put the nasty looking stuff back in for our apples and oranges.

14. Solving Equations!!!