Why do we Need Algebra?

Date: 9/13/96 at 17:45:9
From: Anonymous
Subject: Why do we Need Algebra?

I don't have a specific question, but why do we need algebra? All it 
involves is doing the same process but making it longer.

Date: 9/13/96 at 18:33:41
From: Doctor Tom
Subject: Re: Why do we Need Algebra?

Hi there,

I assume you mean that right now, a lot of the problems look something 
like this:

Solve for x:  5x = 10.

And your teacher is making you do a series of steps when the answer is 
"obviously" 2.

Think of what you're doing in comparison with the training you'd do to 
be a good football player.  What does the coach do?  He doesn't have 
to do full-blown plays with 22 people on the field at first.  You do 
drills - take 5 steps, turn around, and catch a pass. Then try it with 
somebody guarding you, and so on.  You master the little steps so you 
know how to block, how to tackle, how to catch passes, how to fake,
et cetera, because you've done each over and over until you're an 
expert.  Then, when you're playing, you can think about the play and 
you don't think about the details.

For a problem like this:

Find x, y, and z such that:

         x + y + z = 12
       2x - y + 4z = 22
  11x - 61y + 123z = 4533

Is the answer obvious?  But you can get to the answer using a series 
of simple steps of exactly the same sort you used to solve 5x = 10.  
It's a lot of steps, but each is simple.  If you don't have to think 
about the individual steps, but rather how to make progress on the 
larger problem, you'll be able to do it.

I hope this helps.  Be patient -- in not too long, your "drills" will 
start to pay off!

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