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#1 15. 09. 2011 07:39

stuart clark
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modulus equation

solve equation for $x$ in

$\displaystyle { |x|-|x+2|+|x+4|-|x+6|+...-|x+998| =|x+1|-|x+3|+|x+5|-|x+7|+...-|x+999| }$

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#2 20. 09. 2011 16:41 — Editoval pietro (20. 09. 2011 16:53)

pietro
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Re: modulus equation

↑ stuart clark:
Hi,
some fragments

m=2,3
http://www.wolframalpha.com/input/?i=so … 28x%2B3%29

(-oo..-3> V <0...+oo)
============================================


m=6,7
http://www.wolframalpha.com/input/?i=so … 28x%2B7%29

(-oo..-7>V<-4...-3>V <0...+oo)
==============================================

m= 10,11
(-oo..-11>V<-8...-7>V<-4...-3>V <0...+oo)

==============================================

m= j,j+1
(-oo..-(j+1)>V<-(j+1)+3... -(j+1)+4>V..........V<-8...-7>V<-4...-3>V <0...+oo)
simplify
(-oo..-(j+1)>V<2-j to 3-j > V I(2) V I(3) V I(4) V  .... V I(k) V......   V<-8...-7>V<-4...-3>V <0...+oo)
where
I(k) = < (4*k-2)-j .... (4*k-1)-j >
===============================================


"http://www.wolframalpha.com/input/?i=%28-oo%2C+-11]%2C++[-8%2C-7]+%2C+++[-4%2C-3]%2C++[0%2Coo%29"

test for x=0.1

http://www.wolframalpha.com/input/?i=+% … 28-1%29^j+

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