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What range of values of x will satisfy the inequality contd.

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What range of values of x will satisfy the inequality contd. [#permalink]  25 May 2011, 06:04
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Question Stats:

20% (02:56) correct 80% (02:25) wrong based on 5 sessions
What range of values of x will satisfy the inequality |2x + 3| > |7x - 2|?

A. x < (-1/9) or x > 5

B. -1 < x < (1/9)

C. (-1/9) < x < 1

D. (-1/9) < x < 5

E. x < (-1/9) or x > 1

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Re: What range of values of x will satisfy the inequality contd. [#permalink]  25 May 2011, 06:26
two methods here.

1. using the solutions here. x= -3/2 and x= 2/7 are solutions.
check for the regions

a. x<-3/2, b. -3/2<x<2/7 and c. x>2/7

values are a -(2x+3) > (7x-2) giving x <-1/9 hence not a solution.

b (2x+3) > (7x-2) giving x < 1 a solution.

c (2x+3) > -(7x-2) giving x>-1/9 hence the solution is -1/9 < x < 1

or

2. squaring both sides

(2x+3) ^2 > (7x-2)^2

gives 9x^2 -8x - 1 > 0 giving solution -1/9 < x < 1.

Hence C you can use whichever you are comfortable with.
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Re: What range of values of x will satisfy the inequality contd. [#permalink]  25 May 2011, 14:42
Amit,

Thank you, but could you please elaborate why in the option A

"a. x<-3/2,

values are a -(2x+3) > (7x-2) giving x <-1/9 hence not a solution."

the second part - (7x-2) is positive? If we get a number less than -1/9, -10 for instance would not the second part be negative as well?

Regards,
Steve.
Re: What range of values of x will satisfy the inequality contd.   [#permalink] 25 May 2011, 14:42
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