by Shelley Walsh ©2000
Linear Equations are equations involving multiplying and adding and subtracting that have no exponents. You can always solve them by repeated use of a very simple idea.
If two things are equal and you do the same thing to both of them, then they must still be equal.
The game in solving equations is to keep doing this until you get the variable alone on one side of the equation and a number on the other side of the equation, and then for the original equation to be true, this equation has to be true, and this equation tells you exactly what the variable has to be. The only other trick is to decide what operations to do to both sides to get it into this form. To do this, you need to think ahead a little bit and also keep your goal in mind. Always remember that in the end you are trying to get the variable alone on one side of the equation and a number on the other side. If there is an operation done and you want to get rid of it, the best way normally to do this is to do to opposite operation. If you have several operations being done to the variable it normally works best to get rid of the last one done first. Put yourself in the place of the variable and ask if I was the x what is being done to me first and when you are doing this remember the order of operations. A general procedure that will always work with these problems is to first simplify both sides of the equation, and then get all of the variables on one side and all the numbers on the other side, and then divide by the coefficient. But other methods will work as well.