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Which of the following inequalities is equivalent to |2x - |x|| < 3?
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18 Nov 2023, 06:54
18 Nov 2023, 06:54
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33%
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Which of the following inequalities is equivalent to \(|2x-|x||<3\)?
A. \(0<x<2\)
B. \(0<x<3\)
C. \(-1<x<3\)
D. \(0<x<1\)
E. \(-3<x<1\)
A. \(0<x<2\)
B. \(0<x<3\)
C. \(-1<x<3\)
D. \(0<x<1\)
E. \(-3<x<1\)
Joined: 01 Aug 2023
Posts: 30
Given Kudos: 26
Location: India
Concentration: Strategy, Technology
GPA: 3.7
WE:Engineering (Other)
Re: Which of the following inequalities is equivalent to |2x - |x|| < 3?
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19 Nov 2023, 01:52
19 Nov 2023, 01:52
2
Kudos
|2x−|x||<3
It can be written as
1. 2x−|x|<3
2. -(2x-|x|)<3 or -2x+|x|<3
In 1, if x is positive: x<3 and if x is negative: -3x<3 or x>-1. Hence, −1<x<3.
In 2, if x is positive: x<3 and if x is negative: 3x<3 or x<3. Hence, x<3.
In both cases, −1<x<3 is common.
IMO, C
It can be written as
1. 2x−|x|<3
2. -(2x-|x|)<3 or -2x+|x|<3
In 1, if x is positive: x<3 and if x is negative: -3x<3 or x>-1. Hence, −1<x<3.
In 2, if x is positive: x<3 and if x is negative: 3x<3 or x<3. Hence, x<3.
In both cases, −1<x<3 is common.
IMO, C
Re: Which of the following inequalities is equivalent to |2x - |x|| < 3?
[#permalink]
09 Dec 2023, 15:09
09 Dec 2023, 15:09
1
Kudos
singh.00
|2x−|x||<3
It can be written as
1. 2x−|x|<3
2. -(2x-|x|)<3 or -2x+|x|<3
In 1, if x is positive: x<3 and if x is negative: -3x<3 or x>-1. Hence, −1<x<3.
In 2, if x is positive: x<3 and if x is negative: 3x<3 or x<3. Hence, x<3.
In both cases, −1<x<3 is common.
IMO, C
It can be written as
1. 2x−|x|<3
2. -(2x-|x|)<3 or -2x+|x|<3
In 1, if x is positive: x<3 and if x is negative: -3x<3 or x>-1. Hence, −1<x<3.
In 2, if x is positive: x<3 and if x is negative: 3x<3 or x<3. Hence, x<3.
In both cases, −1<x<3 is common.
IMO, C
Could you please explain further?
