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Solving for x

Date: 10/22/96 at 19:57:56
From: Shelby Dotson
Subject: Math, Algebra

Dear Dr. Math, 

How do you solve an equation for x?  Example: x/a = k

I don't get it and I can't find the answer in my book.
My friends in algebra 1 don't know either. Please help! 

         Shelby Ann Dotson

Date: 10/24/96 at 16:47:8
From: Doctor Rob
Subject: Re: Math, Algebra

The question is, what expression can you substitute for x
and make the equation given true?  Can you think of some
expression which, when divided by a, gives x?

If you can't guess, you can use the following method.

You want to change the equation into one of the form x = something.
To make (x/a) into x, we need to "undo" the division by a.  The 
operation that does that is multiplication by a, since if we start 
with any number and divide it by something, then multiply the result 
by the same something, we get the original number back.  Also, if we 
start with any number and multiply it by something, then divide the 
result by the same something, we get the original number back again.

This tells us that we want to multiply the left side of the equation 
by a.  We can't just do that, however, since we want the equation to 
still be true.  We have to multiply *both* sides of the equation by a.  
Then, since equals (x/a and k are equals) multiplied by equals (a and 
a are also equals) give equals, we get

    (x/a) * a = k * a,

or else

    x = k * a.

Does this work?  We can check by seeing if putting k a in the equation 
in place of x gives a true equation:

     (k a)/a = k

is true, all right, since multiplying k by a and dividing by a gives 
back k.

-Doctor Rob,  The Math Forum
Associated Topics:
Middle School Algebra

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