Simplifying an Expression

Date: 04/29/99 at 23:02:48
From: Sid
Subject: Pre-Algebra

Dear Dr. Math,

I am having trouble trying to figure out this homework assignment 
that our "sub" handed out to us today for homework. The homework was 
to figure out some problems by using x or y, but the x and y don't 
have a specific number to them. 

For example: (x+3)+(4x-7)+(x-20). I just can't figure it out.

Date: 04/30/99 at 09:21:00
From: Doctor Rick
Subject: Re: Pre-Algebra

Hi, Sid, welcome to Ask Dr. Math!

This is really pre-algebra - it's a skill you will be using all the 
time in algebra. We call it "simplifying an expression." That means 
basically reducing the number of operations that will be needed to 
find the answer after you know what number the variable x stands for.

Even though you don't know what number x stands for, you know a great 
deal about it because you know it stands for SOME number. You know in 
particular the 3 properties of numbers: commutative, associative, and 
distributive. To simplify your expression, you need all of these.

To start with, the associative property tells you that you can drop 
the parentheses, because it doesn't matter which additions you do 
first.

  x + 3 + 4x - 7 + x - 20

Next, the commutative property tells you that you can swap terms 
around. Let's move all the terms with x in them to the beginning:

  x + 4x + x + 3 - 7 - 20

We can add up the three numbers right away:

  x + 4x + x - 24

Now it's time for the distributive property. Maybe it doesn't look 
like it to you, but there are some "phantom ones" lurking by those 
lone x's:

  1x + 4x + 1x - 24

This is a good thing to keep in mind: multiplying anything by 1 
doesn't change it, so you can stick in a 1 wherever it will help. Now 
you can combine all the numbers that multiply x:

  (1 + 4 + 1)x - 24

Again, add the numbers:

  6x - 24

And we're done! We can't make it any simpler unless we know what 
number x stands for.

Do you get the idea? Try it on your other problems.

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