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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?

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SVP  D
Joined: 03 Jun 2019
Posts: 1877
Location: India
How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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3
21 00:00

Difficulty:   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
Director  V
Status: Manager
Joined: 27 Oct 2018
Posts: 746
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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5
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
##### General Discussion
Manager  B
Joined: 17 Sep 2017
Posts: 100
Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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1
1
Hi, can someone explain the working of this question
Intern  B
Joined: 21 Mar 2019
Posts: 22
Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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Hello,
I am interested too. I don't really know how to tackle this problem. Can someone please give us an explanation ?
Senior Manager  P
Joined: 10 Jan 2017
Posts: 330
Location: India
Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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5
1
Coggi abhishek31,

please fine the attached image, hope i am able to answer the working principle of modulus questions like this.
Attachments 20190806_095709.jpg [ 2.45 MiB | Viewed 1484 times ]

Intern  B
Joined: 21 Mar 2019
Posts: 22
Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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1
Thank you very much ! I understand now !   Manager  B
Joined: 02 Nov 2018
Posts: 54
Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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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 <?
Manager  G
Joined: 06 Feb 2019
Posts: 110
Re: How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?  [#permalink]

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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?

Posted from my mobile device 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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