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Is |x-1|<1? 1. (x-1)^2 is less than or equal to 1 2. x^2

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CEO
Joined: 21 Jan 2007
Posts: 2505
Location: New York City
Is |x-1|<1? 1. (x-1)^2 is less than or equal to 1 2. x^2  [#permalink]

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21 Nov 2007, 02:02
Is |x-1|<1?

1. (x-1)^2 is less than or equal to 1
2. x^2 -1 is greater than 0

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Manager
Joined: 20 Jun 2007
Posts: 145

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21 Nov 2007, 02:55
1
You need the two:

1. (x-1)^2 is less than or equal to 1
This tells you that x is between 0 and 2 (this is the only range of values that will work)

|0-1| is not less than 1
|2-1| is not less than 1
|1-1| is less than 1
Insufficient

2.x^2 -1 >0
so x^2 >1
so x is not between -1 and +1, but could be any other value
Possible solutions:
|-2-1| = 3
|1.5-1| = 0.5
Insufficient

Together:
We know that x is between 0 and 2
We also know that it's not between -1 and +1
So it must be greater than 1 and less than or equal to 2
So it's never less than 1

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Posts: 11029
Re: Is |x-1|<1? 1. (x-1)^2 is less than or equal to 1 2. x^2  [#permalink]

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21 Jul 2017, 06:06
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This discussion does not meet community quality standards. It has been retired.

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Re: Is |x-1|<1? 1. (x-1)^2 is less than or equal to 1 2. x^2   [#permalink] 21 Jul 2017, 06:06
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