Equations and Negatives

Date: 05/23/99 at 19:27:51
From: Bri
Subject: Writing out equations

The problem is 6(-N) = 3(N)+72. I already know that you subtract 3N 
from both sides, but how? How do you subtract a positive N from a -N?

Thanks a bunch! 
-Bri

Date: 05/24/99 at 12:28:47
From: Doctor Peterson
Subject: Re: Writing out equations

Hi, Bri.

There are two things you have to be familiar with to do this problem: 
negative numbers and the distributive property.

The first thing to do is to simplify the equation by removing the 
parentheses. The "6(-N)" can be written as "-6N" by thinking of it as

    6 (-1 * N)

and applying the associative property. Our equation then becomes

    -6N = 3N + 72

Now, as you say, you have to subtract 3N from both sides:

    -6N - 3N = 72

Now we can use the distributive property "in reverse"; but to make it 
clearer for you, we can first rewrite the negatives:

    (-6)*N + (-3)*N = 72

        (-6 + -3)*N = 72

                -9N = 72

Finally, we can divide both sides by -9:
       
                  N = 72/(-9) 
                    = -72/9 
                    = -8

Working with negatives like this can be a little tricky at first, but 
if you think of it this way it should become natural to you with 
practice.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/