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For what values of x is |x - 4| - |x - 3| >= 7?

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For what values of x is |x - 4| - |x - 3| >= 7?  [#permalink]

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New post 02 Dec 2019, 01:30
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

71% (01:39) correct 29% (01:50) wrong based on 134 sessions

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Re: For what values of x is |x - 4| - |x - 3| >= 7?  [#permalink]

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New post 02 Dec 2019, 01:43
I just tested the options

A) Let x=0; 4-3 is not more than seven. Dismiss
B) Let x=3.5; 0.5-0.5 does not satisfy the stem. Dismiss
C) Let x=100; 96-97 does not satisfy the stem. Dismiss
D) Let x=100; 96-97 does not satisfy the stem. Dismiss
E) The only option left

IMO
ans: E
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For what values of x is |x - 4| - |x - 3| >= 7?  [#permalink]

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New post 02 Dec 2019, 20:40
2
Bunuel wrote:
For what values of x is \(|x-4|-|x-3|\geq7\)?


A. \(x\leq3\)

B. \(3\leq x\leq4\)

C. \(x\geq4\)

D. \(x\geq7\)

E. No values of x satisfy this inequality.


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You can also solve it logically.
In |x-4|-|x-3|, whatever happens to x in one MOD will happen to x in 2nd MOD.
So basically x is cancelling out with each other and what you are left with is |-4|-|-3|=4-3=1
So the equation will be equal to 1 whatever be the value of x.
So it will NEVER be \(\geq{7}\)

E
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Re: For what values of x is |x - 4| - |x - 3| >= 7?  [#permalink]

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New post 04 Dec 2019, 22:06
For what values of x is |x−4|−|x−3|≥7
consider three situations x<3 , 3<x<4 , 4<x

\(when x<3\)
-x+4-(-x+3)=1
1 is not greater than or equal to 7
So equation does not holds true for x<3

\(when 3<x<4\)
-x+4-x+3= -2*x+7
check for x=3.9
=-2*3.9+7= -0.8
-0.8 is not greater than or equal to 7
So equation does not holds true for 3<x<4

\(when 4<x\)
x-4-x+3=-1
-1 is not greater than or equal to 7
So equation does not holds true for 4<x

Therefore No value of x satisfies the inequality

Answer: E
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Re: For what values of x is |x - 4| - |x - 3| >= 7?  [#permalink]

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New post 30 Dec 2019, 08:56
Can we not just say that |x-4| and |x-3| are two consecutive numbers and hence the difference can never be other than 1? This takes 5 seconds.
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Re: For what values of x is |x - 4| - |x - 3| >= 7?   [#permalink] 30 Dec 2019, 08:56
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