Doing the Same Thing to Both Sides of an Equation
Date: 10/20/2003 at 22:07:18 From: Mike Subject: equation When I subtract something from one side of an equation do I add it to the other side or do I subtract it from that side also? I'm working on the equation 6(c + 4) = 4c - 18.
Date: 10/21/2003 at 11:36:25 From: Doctor Douglas Subject: Re: equation Hi Mike - Thanks for writing to the Math Forum. Good question! When manipulating equations, you should always do the same thing to both sides. For example, you should subtract the same thing from BOTH sides: 6(c + 4) = 4c - 18 6c + 24 = 4c - 18 no problem yet. 6c + 24 - 4c = 4c - 18 - 4c subtract 4c from BOTH sides 2c + 24 = - 18 But there is another way to look at it, too. You can MOVE something from one side of the equation to the other side, provided you change its sign: 6c + 24 = 4c - 18 6c + 24 - 4c = - 18 We move the +4c to the left, 2c + 24 = - 18 changing the sign in the process. It may seem like this moving process is not performing the same operation on both sides, but it really is. Both sides have had 4c subtracted, just like in the first example. Usually the moving method is a shortcut because you don't have to actually do the arithmetical work on one side. In the second example, we don't have to do the 4c - 4c on the right because we know it must be zero. I hope that explains what is going on. Please write back if you have more questions about this. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.