Simple Algebraic Equations

Date: 5/26/96 at 15:58:8
From: Anonymous
Subject: Simple Algebraic Equations

I know this is a pretty broad topic but I just can't seem to 
understand how you can logically say that 10 + 5x = 110 and have         
x equals -30 when logically x should equal 20. I just don't 
understand.

Lost,
Anacas

Date: 5/28/96 at 0:7:25
From: Doctor Ken
Subject: Re: Simple Algebraic Equations

Hello!

You're absolutely right, in the equation 10 + 5x = 110, the correct 
answer for x is 20.  Whenever you solve an equation, you should be 
able to take your answer and plug it back into the equation and have 
it make sense.  So, if you've got the equation 5x = 80 and you solve 
it and get x = 3, then you know something isn't right when you plug in 
3 for x and get 5 x 3 = 80, which (last time I checked) is way off.

So how can we "show" that the solution to your equation is x = 20?  
Well, here's one way:

10 + 5x = 110            subtract 10 from both sides
     5x = 100            divide both sides by 5
      x = 20

Does that make sense?

-Doctor Ken,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/