Algebra - Solving EquationsDate: 11/03/97 at 23:36:50 From: AVI MANTHA Subject: ALGEBRA Hi, Dr. Math, I am in an enriched Algebra class, and I'm having a hard time solving some of my math problems. Please help me: 4 - 3X = 5 - 6X - 7 7X = 5(X - 12) Please explain the solution step by step. Thank you very much for your help. Avi Date: 11/10/97 at 09:28:19 From: Doctor Allan Subject: Re: ALGEBRA Hello Avi, and thanks for writing to Dr. Math! You do not tell me exactly where you have problems, so I am not sure whether you have problems with these types of equations generally, or if it is just the two problems you mention here. What I will do is give you techniques to use when solving these equations, and then help you with the first of your problems - then you can check out whether that helps you solving the second problem and getting the general picture. When you want to solve an equation you want to find values such that if you substitute these values for x in your equation, you will get something that is true. Let me give you an example: x + 5 = 8 What you need to do is find a value to substitute for x such that you get 8. If you have five apples and you want to have eight apples how many more apples should you buy? That's basically what an equation is all about. So the smart thing to do is to isolate x on one side of the equation and that will tell you the exact value to be substituted. In order to do this you have to remember some rules. The most important one is this: Whatever you do to one side of the equation you should do to the other side. That means if you for instance add 3x to one side you should add 3x to the other side. Furthermore, there is the distributive rule: x(a+b) = (a+b)x = xa+xb This means that when you multiply terms within a parenthesis by x, you multiply x by each term of the parenthesis. That should cover the basics. Now let's go to the first of your problems: 4 - 3x = 5 -6x -7 First notice that 5 - 7 = -2 so you get 4 - 3x = -2 -6x Now you want to isolate x on one side of the equation, so let's subtract 4 from each side of the equation. We get 4 - 3x - 4 = -2 - 6x -4 That is -3x = -6 -6x Since you want the x on one side the thing to do now is to add 6x: -3x + 6x = -6 - 6x + 6x That is 3x = -6 So all you need to do now to isolate x is to divide by 3 on each side: (3x)/3 = (-6)/3 So you get x = -2 I hope this helped you. If you have further questions, please write again and I will try to help you out. -Doctor Allan, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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