Variable Expressions with Parentheses

Date: 9/9/96 at 18:31:41
From: Anonymous
Subject: Variable Expressions with Parentheses

I can complete some problems like this, but often I come up with an 
answer that is completly wrong and do not know why.  How do you solve:

2(x-1) - 3(2 - 3x) - (x + 1)

I can use the distributive property to simplify the first two parts of 
the problem, but them I am lost...

Date: 9/9/96 at 19:17:40
From: Doctor Mike
Subject: Re: Variable Expressions with Parentheses

Hi,
  
The combination of the distributive property with minus signs often 
causes a little bit of confusion.  First let's get to the place where 
I think you are in the problem: 
  
      (2x-2) - (6-9x) - (x+1) 
  
Notice that I have left it in the form of 3 expressions, where 2 of 
them need to be subtracted.  The key thing to remember is to subtract 
BOTH things inside the 2nd and 3rd expressions.  For instance, to 
subtract 6-9x you have to subtract 6 and also subtract -9x.  
The -(-9x) just becomes +9x.  So, after subtracting you get:
  
      2x - 2 - 6 + 9x - x - 1
  
The next step is to combine like terms, that is, get all the x parts 
together and get all the plain numbers together.  So, 
   
      10x - 9 

I hope this helps. 

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