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If |5x - 5| > x - 1, which of the following must be true?

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Bunuel
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If |5x - 5| > x - 1, which of the following must be true? [#permalink] New post  05 Apr 2021, 10:00
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If |5x - 5| > x - 1, which of the following must be true?

A. x < 1
B. x > 1
C. x > 5
D. x < 5
E. None of the above
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Bunuel
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Re: If |5x - 5| > x - 1, which of the following must be true? [#permalink] New post  12 Apr 2021, 21:00
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Bunuel wrote:
If |5x - 5| > x - 1, which of the following must be true?

A. x < 1
B. x > 1
C. x > 5
D. x < 5
E. None of the above


\(|5x-5|>x-1\);

Factor out 5: \(5*|x-1|>x-1\). Notice here that LHS must more than or equal to 0.

If x-1 is negative, then (LHS=positive) > (RHS=negative);
If x-1 is positive, then (LHS=5 times some positive value) > (RHS = that positive positive).
If x-1 is 0 (so if x=1), then LHS = RHS.

Therefore, \(|5x-5|>x-1\) holds true for any value of x, but 1.

Answer: E.
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Re: If |5x - 5| > x - 1, which of the following must be true? [#permalink] New post  05 Apr 2021, 10:21
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|5×-5|>×-1
5x-5>+(×-1) or -(×-1)

If 5×-5>×-1 then 4×-4>0 or ×>1
If 5×-5>-(×-1) then 6×-6>0 or ×>1

So, answer: B

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If |5x - 5| > x - 1, which of the following must be true? [#permalink] New post  25 Sep 2021, 07:55
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Hi Bunuel,

I have a question.
As per the given solution, any value except number "1" should satisfy the equation. So, B i.e. x>1 must be true right?
Please tell me, what am I missing here because in this case we have two answers which seem correct : B and E.
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Bunuel
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Re: If |5x - 5| > x - 1, which of the following must be true? [#permalink] New post  25 Sep 2021, 09:12
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Yogananda wrote:
Hi Bunuel,

I have a question.
As per the given solution, any value except number "1" should satisfy the equation. So, B i.e. x>1 must be true right?
Please tell me, what am I missing here because in this case we have two answers which seem correct : B and E.


The question asks: "which of the following must be true?" x > 1 is not necessarily true because x could be any number less than 1, for example, 1/2, or -1000...
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If |5x - 5| > x - 1, which of the following must be true? [#permalink] New post  Updated on: 25 Sep 2021, 09:37
Asked: If |5x - 5| > x - 1, which of the following must be true?

Case 1: x >= 1
5x - 5 > x - 1
4x > 4
x > 1
x = 1 is not possible since 0 > 0 does not hold true

Case 2: x<1
5 - 5x > x - 1
6x < 6
x < 1

Combining
|5x - 5| > x - 1 holds true for all x but 1.

IMO E

Originally posted by Kinshook on 25 Sep 2021, 09:33.
Last edited by Kinshook on 25 Sep 2021, 09:37, edited 1 time in total.
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IanStewart
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Re: If |5x - 5| > x - 1, which of the following must be true? [#permalink] New post  25 Sep 2021, 09:35
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Bunuel wrote:
If |5x - 5| > x - 1, which of the following must be true?


A slightly different solution to Bunuel's: |5x - 5| = 5|x - 1|. Unless x= 1, |x - 1| is positive, in which case 5|x - 1| > |x - 1| (if you multiply a positive number by 5, it gets bigger), and naturally |x - 1| > x- 1. Putting those two inequalities together, if x isn't equal to one, 5|x - 1| > x - 1, and |5x - 5| > x - 1. So the inequality is true for every value of x except x= 1, and the answer is E.
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IanStewart
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Re: If |5x - 5| > x - 1, which of the following must be true? [#permalink] New post  25 Sep 2021, 09:36
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Kinshook wrote:
Case 2: x<1
5 - 5x > x - 1
6x > 6
x > 1
Not feasible

x > 1

IMO B


The line I highlighted in red above should read "6 > 6x", so you should reach the conclusion that "x < 1" in this case.
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Re: If |5x - 5| > x - 1, which of the following must be true? [#permalink] New post  17 Nov 2023, 19:33
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Re: If |5x - 5| > x - 1, which of the following must be true? [#permalink]
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