Doubling Opposite Integers
Date: 04/19/98 at 13:49:55 From: Renee Bailey Subject: Integers On a number line, a certain integer is 24 units away from the double of its opposite. What is the integer? I started to look at different integers and the double of their opposites, for example 12 and 21(2), which are 30 units apart, and 43 and 34(2), which are 25 units apart, etc. However, I did this with about 50 different numbers and still have not found two that are 24 units apart. So I was wondering, is there an equation that I can use to solve this problem, and if so what? Or do I have to keep doing trial and error?
Date: 04/19/98 at 14:03:16 From: Doctor Rothman Subject: Re: Integers Hi Renee. Let's actually draw a number line and look at where the integer, its opposite, and the double of its opposite might lie. Remember that the "opposite" of a number implies that you multiply the number by -1, not that you reverse the digits. Let's call the integer P, because we'll start out assuming it's positive (although the problem doesn't say it has to be). So here's the number line: -2P -P 0 P -|-------------|----------------.----------------|----------------- P is our integer, -P is its opposite, and -2P is the double of its opposite. If we then say that the distance between P and -2P is 24, then P - (-2P) = 24. Now solve this equation for P. When you check this value for P, is it indeed 24 units away from "double its opposite," -2P? There's still another part to this problem though. We assumed the integer was positive, but what if it was negative? I'm going to let you figure that out on your own. Good luck! -Doctors Naomi and Rothman, The Math Forum http://mathforum.org/dr.math/
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