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# Another Look at Something.....????

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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.........

Sir CPhill

CPhill  Jul 31, 2014

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Ok Chris - I will let you have the last word.  The term is a little ambiguous.

Melody  Jul 31, 2014
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There's an interesting discussion of the meaning of "difference" in a math context here: http://mathforum.org/library/drmath/view/63137.html

Alan  Jul 31, 2014
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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

Melody  Jul 31, 2014
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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.....

CPhill  Jul 31, 2014
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