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### Solving -X = 3

```
Date: 10/26/98 at 18:40:06
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.

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/
```
Associated Topics:
Middle School Algebra
Middle School Negative Numbers

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