Solving -X = 3

Date: 10/26/98 at 18:40:06
From: Tyler Whitehead
Subject:  -x = 3

Please tell me how to get the answer to -x = 3. I have no idea how a 
negative can equal a positive.

Date: 11/05/98 at 17:06:19
From: Doctor Roya
Subject: Re: -x = 3

Dear Tyler,

Thank you for writing to Dr. Math.

We are going to try to solve this problem backwards. By that I mean, 
we are going to look at the answer first and work our way back to the 
original problem.

Let's look at the following example: 3 is a positive number. If we 
multiply 3 by -1, we get -3, which is a negative number. We say that 
-3 is the opposite of 3.  

In the same way, 3 is the opposite of -3. How, you may ask? Well, just 
do the same thing. Multiply -3 by -1. We get (-1)(-3) = 3. 

If we drop the 1 in this new equation (we are allowed to drop the 1, 
since 1 times any number is that same number), we end up with:
   
   - -3 = 3
 
This is becoming more familiar, isn't it?  

Now, if we replace -3 with a variable (unknown) X, we end up with:

   - X = 3 

which looks just like your problem.

Going back to your question:

If we read the equation (-X = 3), it says: We have a number X, that 
when we multiply by -1 the result is number 3. What number does X 
represent? 

Remember that (-1)(X) = 3 is really the longer way of writing the same 
equation. I hope that you now see how X must be a negative number. In 
fact X is equal to -3. 
 
Please keep in mind that X stands for a number. That number could be a 
positive number or a negative number. X is just a place holder. Please 
write back if you still have questions.

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