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/
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