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

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SVP
Joined: 03 Jun 2019
Posts: 1515
Location: India
How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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07 Jul 2019, 23:42
2
12
00:00

Difficulty:

95% (hard)

Question Stats:

37% (02:43) correct 63% (02:47) wrong based on 93 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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08 Jul 2019, 03:59
3
3
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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Senior Manager
Joined: 10 Jan 2017
Posts: 253
Location: India
Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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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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20190806_095709.jpg [ 2.45 MiB | Viewed 605 times ]

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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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04 Aug 2019, 02:45
1
1
Hi, can someone explain the working of this question
Intern
Joined: 21 Mar 2019
Posts: 19
Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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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 ?
Intern
Joined: 21 Mar 2019
Posts: 19
Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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05 Aug 2019, 23:44
Thank you very much ! I understand now !
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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