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# For what values of x is the following inequality

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Senior Manager
Joined: 30 Aug 2003
Posts: 330
Location: BACARDIVILLE
Followers: 1

Kudos [?]: 1 [0], given: 0

For what values of x is the following inequality [#permalink]  02 Feb 2004, 15:48
For what values of x is the following inequality 3x-(2/x)>1 true?
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Pls include reasoning along with all answer posts.
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Manager
Joined: 25 Jan 2004
Posts: 92
Location: China
Followers: 1

Kudos [?]: 2 [0], given: 0

(1, +inf) U (-2/3, 0)
SVP
Joined: 30 Oct 2003
Posts: 1794
Location: NewJersey USA
Followers: 5

Kudos [?]: 43 [0], given: 0

x < 2/3 and x > 1
( x - 1) ( x-2/3 ) > 0
Manager
Joined: 25 Jan 2004
Posts: 92
Location: China
Followers: 1

Kudos [?]: 2 [0], given: 0

lets assume x = -1, given x < 2/3

3(-1) -2/(-1) = -1, which is not greater than 1
Manager
Joined: 04 Jun 2003
Posts: 63
Followers: 1

Kudos [?]: 0 [0], given: 0

agree with Zhung Gazi

x E (1,inf) U (-2/3,0)
In this inequality, the cirtical point of 0 is very important.

Manager
Joined: 25 Jan 2004
Posts: 92
Location: China
Followers: 1

Kudos [?]: 2 [0], given: 0

3x - (2/x) > 1
(3x^2 - 2)/x > 1
(3x^2 -x -2)/x > 0

(3x+2)(x-1)/x > 0

(3x+2)x(x-1)/ x^2 > 0

(3x+2)x(x-1) > 0
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