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Absolute modulus : A better understanding

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Re: Absolute modulus : A better understanding [#permalink]

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New post 08 Aug 2017, 05:11
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AkshayKS21 wrote:
I wonder why I didn't come across this before...
Brilliant post.
I used only first method-always, and that is why struggled with 2 and 3 mod questions.
And amazing work on "How many solutions does the equation with more than 1 mod have". Made my life easier.

A big big big Thank You! :)


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Re: Absolute modulus : A better understanding [#permalink]

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New post 15 Aug 2017, 05:43
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chetan2u wrote:
periyar22 wrote:
This is a very confusing method of solving. What is rear? I cant believe this person who spells rare as rear is an expert


Mr periyar,
Firstly, these are the methods used to solve modulus. So, if you find them confusing, you will have to learn them or leave the topic or invent a new method to solve it.
Secondly this post is related to quant, and I hope you are not mistaking this to be a verbal post, as you seem to be more interested in spellings. Thankfully, you found only one mistake in the big post above. But it is surprising, you could not avoid a mistake in even a single line you have written in last two years. It is not cant but can't.
Anyway, experts badge does not mean anyone should follow what he writes and in the same way, it is not necessary if an intelligent person but without a expert badge, like you, writes people will not follow. Please use this forum and assist others and surely people will follow you more than they follow any expert.
By the way, I will not edit rare and rear as it is a mark of your keen observation.




chetan2u
bro

What is more, it is not correct to say, I can't believe this person....bla bla bla.... is an expert, the correct way, however, to say so is, I can't believe this person ...bla bla bla... to be an expert...

So, bro, just forget such negative comments, and keep posting your valuables ...

thanks :)
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Re: Absolute modulus : A better understanding [#permalink]

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New post 22 Sep 2017, 07:28
gmatexam439 wrote:
Thank you Chetan for this. I would like to share an alternate method for solving absolute equations which can be used for as many variables: [I used this while persuing my engg.]

While solving the below equation:
|x+3|-|4-x|=|8+x|

=> |x+3|-|4-x|-|8+x|=0
Therefore the critical points will be x=-8,-3 and 4

Case 1. Now when x<-8 on the number line
|x+3| will open with a -ve sign, |4-x| will open with a +ve sign and |8+x| will open with a -ve sign
Therefore, equation will be
=> -x-3-4+x+8+x=0
=> x=-1; Now if we notice this value of x doesn't match with the case value i.e. x<-8 therefore this is not a correct answer.

Case 2. Now when -8<x<-3 on the number line
|x+3| will open with a +ve sign, |4-x| will open with a +ve sign and |8+x| will open with a +ve sign
Therefore, equation will be
=> x+3-4+x-8-x=0
=> x=9; Now if we notice this value of x doesn't match with the case value i.e. -8<x<-3 therefore this is not a correct answer.

Case 3. Now when -3<x<4 on the number line
|x+3| will open with a +ve sign, |4-x| will open with a +ve sign and |8+x| will open with a +ve sign
Therefore, equation will be
=> x+3-4+x-8-x=0
=> x=9; Now if we notice this value of x doesn't match with the case value i.e. -3<x<4 therefore this is not a correct answer.

Case 4. Now when x>4 on the number line
|x+3| will open with a +ve sign, |4-x| will open with a -ve sign and |8+x| will open with a +ve sign
Therefore, equation will be
=> x+3+4-x-8-x=0
=> x=-1; Now if we notice this value of x doesn't match with the case value i.e. x>4 therefore this is not a correct answer.

Therefore there is no solution to this equation.



I think in case 2: X should be equal to -15 not 9.
Since -8<x<-3,
(x+3) will be NEGATIVE not positive,
Therefore, equation will be
=> -(x+3)-(4-x)-8-x=0
=> -x-3-4+x-8-x=0
=> -15=x
not that it really matters coz the answer is still invalid but thought I'd still point it out.
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Re: Absolute modulus : A better understanding [#permalink]

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New post 26 Oct 2017, 06:15
chetan2u & Bunuel Thanks a lot for being in this forum. God Bless you!
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Re: Absolute modulus : A better understanding [#permalink]

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New post 14 Nov 2017, 04:24
how to apply such method in the actual test?
Or, is this theory that helps to understand the concept of the absolute modulus.
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Re: Absolute modulus : A better understanding [#permalink]

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New post 28 Jan 2018, 22:12
chetan2u wrote:
AR15J wrote:
Hi Chetan,

First of all, thanks for sharing this information. In graphical method, I could not get how did you draw the graph for two modes at one side (x+3|-|4-x|) . My question might be silly but I could not get it. Please explain. Thanks once again.


Hi,

The LHS is|x+3|-|4-x|...
Take this to be equal to y, so y=|x+3|-|4-x|•••••
Now find y for different values of x..
When x=0, y=|0+3|-|4-0|=-1...
When x=1, y=|1+3|-|4-1|=1...
For all values of x as 7 & above 7, y will be a constant 7... and below -7, y will be -7...
You can draw the graph with these points..


So can I say the method is more like plug and test method? Or is there more genuine way to find the graph?
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Re: Absolute modulus : A better understanding [#permalink]

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New post 01 Apr 2018, 23:29
Bunuel wrote:
udbhav2412 wrote:
nice post and exactly what i was looking for :)


In addition to Chetan's excellent post on absolute values, you can find the following topics useful:



For other topics please refer to ALL YOU NEED FOR QUANT ! ! !.

Hope it helps.


Thank you Bunuel. Exactly what I was looking for.
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Re: Absolute modulus : A better understanding   [#permalink] 01 Apr 2018, 23:29

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