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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
3
21
00:00
A
B
C
D
E

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  95% (hard)

Question Stats:

38% (02:37) correct 62% (02:39) wrong based on 159 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
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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]

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New post 23 Sep 2019, 04:10
J2S2019 wrote:
Coggi abhishek31,

please fine the attached image, hope i am able to answer the working principle of modulus questions like this.


Thanks a lot. I get everything except for one thing:

how do you determine the ranges inequality signs? You had:

x<3, 3x<5, 5x<11 and x>11

How did you determine it's ≤ for some and not just <?
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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 28 Oct 2019, 06:41
The thing is to understand that |x-3| means:
The distance between x and 3. So the given inequality states that the combined distance between x and 3 plus distance between x and 5 is less than distance between x and 11.
We can use the number line to easily count that there are 9 such x:
-2,-1,0,1,2,3,4,5,6.

Does it help?

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Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?   [#permalink] 28 Oct 2019, 06:41
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