One Variable Equations

Date: 04/26/97 at 08:43:39
From: Eliza Straks
Subject: Equations

Hi!

I have tried to figure out how to solve 14 = 7d - 2 + d, but when I 
do, I put the wrong numbers all in the wrong spots and I come out with 
the wrong answer.

Date: 04/26/97 at 23:14:30
From: Doctor Mike
Subject: Re: Equations

Dear Eliza,
  
Let's start out with a simplification on the right side. The letter 
"d" stands for a mystery number. It's a perfectly good number; you 
just don't know what it is.  The right side says: 
  
   You have 7 times whatever d is, then 2 is taken away, and then 
   another d is added on.
  
A simpler way to look at that is that you have 8 times whatever d is, 
with 2 taken away. This is because you can add 7d to d, which equals 
8d. That's an important kind of simplification for you to know how to 
do. Now the equation is: 
   
   14 = 8d - 2
    
That looks less cluttered and easier to get a grip on.  Now here is a 
*really* important thing for you to know that you can do. Whenever 
you have an equation, that's a guarantee that the things on the left 
of the equal sign and the things on the right of the equal sign are 
exactly the same. The number 14 is the same as the expression 8d-2.  
So, anything you do to 14 you can also do to 8d-2 and the two results 
are still going to be equal; you are *still* going to have a true 
equation. Let's see how that will look if we "add 2" to both sides, 
getting: 
  
   14 + 2  =  8d - 2 + 2
    
There's some major simplification we can do here, right?  Part of the 
simplification is just adding the 2 numbers on the left side, and then 
there's the fact that a number added to its negative is zero, so it 
all winds up: 
   
   16  =  8d   
   
Now let's divide both sides by 8, which we can do, and still get a 
true equation: 

    16       8d 
   ----  =  ----
     8        8
   
And if we simplify this, we get yet another true equation: 
   
       2  =  d 
  
Not only is this a true equation, but it is the answer!
  
I hope this helps.   

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