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Absolute modulus : A better understanding

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Joined: 02 Aug 2009
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Re: Absolute modulus : A better understanding  [#permalink]

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New post 06 Nov 2019, 20:09
ccheryn wrote:
chetan2u

i dont know whether somebody asked this question already, if so please redirect me there,

i dont know how you drew that 3 modulus graphical method..

especially the LHS, as RHS side is easy as |8+x|

thanks in advance



Hi,

while you are drawing the graph for LHS, just substitute values of x..
|x+3|-|4-x|..
x=1...|1+3|-|4-1|=4-3=1
x=2...|2+3|-|4-2|=5-2=3
x=5..|5+3|-|4-5|=8-1=7..
x=6..|6+3|-|4-6|=9-2=7...So any value above 4 will give the LHS as 7

Similarly any value <-4 will give LHS as -7
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Re: Absolute modulus : A better understanding  [#permalink]

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New post 06 Nov 2019, 20:18
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philippi wrote:
chetan2u

Great post, thanks!

Could you elaborate how come:

ii) -(x+2)+2x=3.. x-2=3..x=5...
but if we substitute x=5 in |x+2| + 2x= 3..... |x+2| will turn out to be a negative value so discard.

How will it turn negative if we substitute with 5? And what will become neg. exactly?

Thanks in advance!



Hi, we take x+2 <0, so |x+2|=-(x+2)...
we then get x=5, and when we put x=5 in x+2 = 7, (x+2) becomes>0..
But we had taken |x+2|=-(x+2)...|5+2|=-(5+2)=-7, so |x+2| has become NEGATIVE

Otherwise just take that you started with assumption that x+2<0, but x=5 gives x+2>0, so discard
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Re: Absolute modulus : A better understanding  [#permalink]

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New post 14 Nov 2019, 12:08
This post is the best. Thanks for the great work chetan2u
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Re: Absolute modulus : A better understanding  [#permalink]

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New post 08 Dec 2019, 01:14
Hello,,

First of all I really would like to thank you Sir. This is much needed post.

but I have a doubt in using critical point method when it involves inequality sign and variables on other side
ex-- what is the range of x when |x-5|+|x+7|< 2x+4.....so if I solve it using the critical point value we can see we will have to check for the x<-7 , -7<x<5 and x>5....so my question is that IN ANY CASE WILL WE HAVE TO CHANGE THE INEQUALITY SIGH OR THE INEQUALITY SIGN WILL REMAIN AS IT IS IRRESPECTIVE OF X BEING POSITIVE OR NEGATIVE?

Thanks in advance
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Re: Absolute modulus : A better understanding   [#permalink] 08 Dec 2019, 01:14

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