Simplifying an Expression

Date: 05/04/99 at 21:31:10
From: (anonymous)
Subject: Using a reciprocal to solve an equation

I have a problem that is very hard for me:

9x - 3x + 7 - 4x + y - 3

Iahamed@aol.com

Date: 05/05/99 at 11:56:20
From: Doctor Rick
Subject: Re: Using a reciprocal to solve an equation

Hi,

This time you're not asking about equations. This is an expression (it 
has no equals sign), and I presume you are supposed to simplify it.

  9x - 3x + 7 - 4x + y - 3

What you want to do is to reduce the number of operations as much as
possible, and to reduce the number of times each variable appears as 
much as possible. The first thing you can do is to use the 
commutativity of addition to move the terms around. I will move all 
the terms containing x to the left, followed by all the terms 
containing y, then all the numbers without a variable.

  9x - 3x - 4x + y + 7 - 3

Now you can add the numbers at the right: 7 - 3 = 4. Let's also 
combine the terms containing x, using the distributive property:

  (9 - 3 - 4)x + y + 4

Add the numbers in the parentheses:

  2x + y + 4

That's as much as we can do. We have one term with each variable and 
one with neither, and there is nothing we can do to combine these.

If you have trouble with subtraction, you can rewrite a subtraction as 
addition of a negative number:

  9x - 3x = 9x + (-3x)

This way you won't get confused when you commute terms.

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