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How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?

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How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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New post 07 Jul 2019, 23:42
2
12
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A
B
C
D
E

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Question Stats:

36% (02:38) correct 64% (02:44) wrong based on 84 sessions

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How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?

A. 7
B. 8
C. 9
D. 10
E. 11

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Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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New post 08 Jul 2019, 03:59
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we have 4 ranges to examine:
at (\(x≥11\)) ,---------> \(x-3+x-5<x-11\) --> (\(x<-3\)) --------------> no common valid values
at (\(11>x≥5\)) ,--> \(x-3+x-5<11-x\) --> (\(x<6.33\)) ------------> 5,6 are common
at (\(5>x≥3\)) ,----> \(x-3+5-x<11-x\) --> (\(x<9\)) ----------------> 3,4 are common
at (\(3>x\)) ,----------> \(3-x+5-x<11-x\) --> (\(x>-3\)) --------------> -2,-1,0,1,2 are common

so we got 9 values C
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Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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New post 04 Aug 2019, 02:45
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Hi, can someone explain the working of this question
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Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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New post 05 Aug 2019, 20:41
Hello,
I am interested too. I don't really know how to tackle this problem. Can someone please give us an explanation ?
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Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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New post 05 Aug 2019, 21:31
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Coggi abhishek31,

please fine the attached image, hope i am able to answer the working principle of modulus questions like this.
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Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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New post 05 Aug 2019, 23:44
Thank you very much ! I understand now ! :) :) :thumbup:
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Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?   [#permalink] 05 Aug 2019, 23:44
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