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#1 2016-07-01 01:16:51

sisyphus
Member
Registered: 2016-05-15
Posts: 26

Inequality with two absolute values

Hello, i just can't get out of the absolute value blackhole lol. The book i'm reading gave me this exercise, but no previous examples how to solve an inequality with two absolute values, so this is what i tried:

|x -3| - |2x +1| < 0

1) if x > 3

      (x-3) - (2x +1) < 0
      x > -4

2) if x < 3 and x >= 0

    -(x-3) - (2x + 1) < 0
     x > 2/3

3) if < 0

   -(x-3) + (2x +1) < 0
    x < -4

The answer given in the book is (-∞, -4) U (2/3, ∞), so all the "if" clauses are false (or at least the first one is). Why? And i'm kind of ashamed to admit, but i'm still not sure of what is it that i'm searching with these absolute value inequalities.

Last edited by sisyphus (2016-07-01 02:26:43)

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#2 2016-07-01 02:08:38

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Inequality with two absolute values

(1) if x>3 then x>-4 It automatically satisfies the condition. Range x>3 is relevant.
(2) if x<3 and x>-1/2
-(x-3)-(2x+1)<0
x>2/3
This should only mean -1/2<x<2/3  does not exist. 2/3<x<3 is valid zone.
(3) x<-1/2
-(x-3)+(2x+1)<0
x+4<0  x<-4 the range  -4<x<-1/2 does not exist.
so the valid range is (-infinity ,-4) U(2/3 ,infinity)


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#3 2016-07-01 02:54:36

sisyphus
Member
Registered: 2016-05-15
Posts: 26

Re: Inequality with two absolute values

I think i could do a few of these after looking at your answer for an hour, but i still don't understand what is it that i'm searching here.

Edit:

Never mind the help part, can anyone point me to an easy to understand, but in depth source that explains absolute values, absolute value equalities,  absolute value inequalities, absolute value functions to an ape like creature like me. I'm already stuck at this subject for a few weeks, even though i can solve most of the problems, i'm just going through the paces without really understanding what is happening.

Last edited by sisyphus (2016-07-01 03:47:30)

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#4 2016-07-01 04:11:48

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Inequality with two absolute values

(1) if x>3 then x>-4  You have to simply find the intersection of these two to find the valid range. similarly others.
I feel nothing special about absolute values. write it as per the definition and see what follows.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#5 2016-07-01 04:27:25

sisyphus
Member
Registered: 2016-05-15
Posts: 26

Re: Inequality with two absolute values

Thanks, i guess i will refer to your example in this thread when i'm stuck with a similar problem.

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#6 2016-07-01 17:15:57

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Inequality with two absolute values

Generally the relations,inequalities show up on functions, not on x itself.The inequalities here are simply "made up" and not real problems.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Offline

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