Checking Equations

Date: 01/30/2001 at 15:13:50
From: Stephanie Jackson
Subject: Checking equations

I know how to solve an equation, but I can't figure out how to check 
it to see if I have the right answer.

Example:  16b-6.5 = 9.5

This is how I do it.
   
 16b-6.5 = 9.5
    +6.5  +6.5
      0 16.0
 16b = 16
 16/16 = 1
But I'm not sure how to check it to make sure it's right. Please help.

Date: 01/30/2001 at 18:09:02
From: Doctor Wilson
Subject: Re: Checking equations

Dear Stephanie,

The steps you are taking to solve the equation are correct. However, 
what do you get after you divide both sides by 16? On the one side, 
you get b, and on the other, you have 1. So, the solution you obtain 
is b = 1. 

Now, to check the solution, you simply plug your answer back into the 
original equation to see if it actually works.

In this case, you get:

 16b - 6.5 = 9.5 (original eq)
16*1 - 6.5 = 9.5 (plugging in b = 1)
  16 - 6.5 = 9.5
       9.5 = 9.5

Notice that you get a true equation: 9.5 = 9.5. This means that the 
solution b = 1 works.

I hope that answers your question.

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