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If |x - 5| + |x - 7| < 4, what is the range of values of x.

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If |x - 5| + |x - 7| < 4, what is the range of values of x.  [#permalink]

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New post Updated on: 13 Sep 2018, 20:39
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If |x - 5| + |x - 7| < 4, what is the range of values of x.

A) 4 < x < 8
B) -4 < x < 8
C) 3 < x < 5
D) -8 < x < -4
E) -4 < x < 4

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Originally posted by divyajoshi12 on 13 Sep 2018, 09:57.
Last edited by Bunuel on 13 Sep 2018, 20:39, edited 2 times in total.
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Re: If |x - 5| + |x - 7| < 4, what is the range of values of x.  [#permalink]

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New post 13 Sep 2018, 10:01
divyajoshi12 wrote:
If |x-5|+|x-7|<4, what is the range of values of x(PS)

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divyajoshi12, Please post the Answer choices.
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Re: If |x - 5| + |x - 7| < 4, what is the range of values of x.  [#permalink]

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New post 13 Sep 2018, 11:05
divyajoshi12 wrote:
If |x-5|+|x-7|<4, what is the range of values of x.

A) 4<x<8
B)-4<x<8
C) 3<x<5
D)-8<x<-4
E)-4<x<4

Posted from my mobile device


|x-5|+|x-7|<4
x-5+x-7<4
2x-12<4
2x<16
x<8 -----(1)

-x+5-x+7<4
-2x+12<4
-2x<-8
x>4 -----(2)
Combining (1) and (2)
4<x<8
Answer A.
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Re: If |x - 5| + |x - 7| < 4, what is the range of values of x.  [#permalink]

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New post 14 Sep 2018, 05:42
souvonik2k wrote:
divyajoshi12 wrote:
If |x-5|+|x-7|<4, what is the range of values of x.

A) 4<x<8
B)-4<x<8
C) 3<x<5
D)-8<x<-4
E)-4<x<4

Posted from my mobile device


|x-5|+|x-7|<4
x-5+x-7<4
2x-12<4
2x<16
x<8 -----(1)

-x+5-x+7<4
-2x+12<4
-2x<-8
x>4 -----(2)
Combining (1) and (2)
4<x<8
Answer A.


Hi,

Can you explain the same question using intersection point method. I mean using "x < 5, 5 < x < 7, x > 7".
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Re: If |x - 5| + |x - 7| < 4, what is the range of values of x.  [#permalink]

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New post 25 Mar 2019, 21:11
x<5

-x+5-x+7 < 4
4<x<5

5<x<7

Valid

x>7

x-5+x-7<4
x<8

So, 4<x<8 Ans
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Re: If |x - 5| + |x - 7| < 4, what is the range of values of x.   [#permalink] 25 Mar 2019, 21:11
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If |x - 5| + |x - 7| < 4, what is the range of values of x.

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