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# Which of the following is equivalent to 0 < x < 2?

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Math Expert
Joined: 02 Sep 2009
Posts: 60591
Which of the following is equivalent to 0 < x < 2?  [#permalink]

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20 Nov 2019, 00:40
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Difficulty:

25% (medium)

Question Stats:

66% (01:01) correct 34% (00:57) wrong based on 81 sessions

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Which of the following is equivalent to $$0 < x < 2$$?

A. $$x=1$$

B. $$|x|<1$$

C. $$|x|<2$$

D. $$|x+1|<1$$

E. $$|x-1|<1$$

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Intern
Joined: 27 Jul 2018
Posts: 20
Which of the following is equivalent to 0 < x < 2?  [#permalink]

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20 Nov 2019, 03:56
|x-1|<1

1. (x-1)<1
= x<1+1 = x<2

2. -(x-1)<1
= -x+1<1
= -x<1-1 = -x<0 = x>0

Combining workings 1 and 2 yields: 0<x<2 which is equal to the expression in the question '0<x<2'

Intern
Joined: 02 Nov 2019
Posts: 2
Which of the following is equivalent to 0 < x < 2?  [#permalink]

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20 Nov 2019, 14:20
| x-1 | < 1

Solve: x-1=0 -> x=1

if x> 1 then |x-1| is positive: x-1<1 and x<2
if x<1 then |x-1| is negative: -(x-1) < 1 which gives -x +1<1 and -x < 0 (multiplie times *-1 to reverse inequality) x>0

To recap we have x<2 and x>0 which gives 0<x<2 which is the inequality in the question.

Which of the following is equivalent to 0 < x < 2?   [#permalink] 20 Nov 2019, 14:20
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