+128406 This problem has been bothering me this evening....(I'm weird like that).........http://web2.0calc.com/questions/the-difference-between-twice-a-number-and-8-is-twenty-more-than-nine-times-the-number-find-the-number#r15
Originally....I thought ND's answer of -4 was incorrect.....maybe it wasn't.....!!!
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In his (or her, as the case may be) post, Anonymous seems to imply that the "difference" between two numbers is as follows: (I quote directly)....
"...I think that the 'difference' between two numbers is the modulus of one number minus the other, that is, the 'difference' between two numbers is a positive number....."
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Let's examine this a little more closely. If I asked you to take minus 3 and subtract a positive 10 from it.....what would the "difference" be??? 13?? Nope......If we on the forum believed that, we would run into some serious problems - in short order. The "distance" between these two numbers is a positive number, but not the "difference." In this case, a negative number definitely ensues from calculating the "difference."
Thus, Anonymous's assertion that ..." 2N-8 implies that 2N is greater than 8" might not be so.....
Sorry.....I'll have to side with NimjaDevo's original answer of -4 as being a correct answer to the original statement of the problem. We may have a semantics issue here with regard to the exact order of subtraction on the left side of the equation.....is it..... 2N - 8 or 8 - 2N ????
Only your hairdresser knows for sure.........
Your Humble Servant,
Sir CPhill
+33614 There's an interesting discussion of the meaning of "difference" in a math context here: http://mathforum.org/library/drmath/view/63137.html
+118608 This was the question
the difference between twice a number and 8 is twenty more than nine times the number. find the number
now you think that the number is -4
The difference between twice a number and 8. Well twice the number is -8.
Umm what is the difference - this is causing all the problem.
So Chris, you think that the difference between -8 and 8 is -8-8=-16
20 more than 9 times the number is -36+20=-16
So Chris you must think the difference between 6 and 4 is different from the difference between 4 and 6?
Mmm If you have pile of 6 apples and I have a pile of 4 apples the the difference the piles is 2 apples.
Isn't it the same answer if I say you have 4 apples and I have 6 apples? Isn'tthe difference still 2 apples?
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I also have given more thought to this question.
I started my solution with
|2x-8| = 9X+20
this lead to the 2 solutions x=-4 and x= -12/11
These were tested and x=-4 was dismissed. Now I should have dismissied this answer without the checking.
Anonymous probably already worked through this but I am slack about working out what other people are telling me so I am trying to work through it myself. Sorry anonymous, I do not mean any offense by this.
Now since 9x+20 is equal to an absolute then it must be >=0
$$\\9x\ge-20\\
x\ge-20/9\\
x\ge\;-2\frac{2}{9}$$
So this excludes x=-4
+128406 Thanks for the reference, Alan....
So it appears that "Dr. Peterson" - if I read Alan's referenced article correctly - tends to side with Melody's "real world" interpretation of "difference" as being poisitve. But, he also admits that some ambiguity exists - that a "textbook" convention of a negative answer is acceptable, as well. Which is exactly what I was trying to imply......that the way we might interpret the left side of the equation may influence our "answer." Thus, as I stated, NDs solution is "an" answer - but not neccessarily the answer anymore than -12/11 is the answer.....
