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PS : inequalities

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Senior Manager
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PS : inequalities [#permalink]

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New post 03 Jun 2009, 14:20
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Which of the following inequalities has a solution set that when graphed on the number line, is a single segment of finite length?
A. x^4>=1
B. x^3<=27
C. x^2>=16
D. 2<=IxI<=5
E. 2<=3x+4<=6

[spoiler]A. x^4>=1=>(x^4-1)>=0=>(x^2-1)(x^2+1)>=0=>(x+ 1)(x-1) (x^2+1)>=0
(x^2+1)>0, so (x+1)(x-1)>=0 =>x<-1,x>1
B. x^3<=27=>(x^3-3^3)<=0=>(x-3)(X^2+3x+3^2)<=0, with d=b^2-4ac we can know that (X^2+3x+3^2) has no solution, but we know that (X^2+3x+3^2)=[(x+3/2)^2+27/4]>0, then, (x-3)<=0, x<=3
C. x^2>=16, [x^2-4^2]>=0, (x-4)(x+4)>=0, x>4,x<-4
D. 2<=IxI<=5, 2<=IxI, x>=2, or x<=2
IMO E[/spoiler]
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Re: PS : inequalities [#permalink]

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New post 03 Jun 2009, 20:30
amolsk11 wrote:
Which of the following inequalities has a solution set that when graphed on the number line, is a single segment of finite length?
A. x^4>=1
B. x^3<=27
C. x^2>=16
D. 2<=IxI<=5
E. 2<=3x+4<=6


For me it's B as only this equation have a single solution of x = 3. Rest all have mutiple solutions.

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Re: PS : inequalities [#permalink]

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New post 03 Jun 2009, 20:36
IMO E.

-2/3<=x<=2/3, all other will give more than one segments of finite and infinite lengths.

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Re: PS : inequalities [#permalink]

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New post 04 Jun 2009, 01:20
one more for E..

only this equation has a line with finite length..

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Re: PS : inequalities [#permalink]

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New post 05 Jun 2009, 02:08
I've absolutly no clue of how to approach this ques.Can anyone please explain each of the answer choices?I tried folowing the first post but somehow got lost inbetween.Appreciate the help.
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Re: PS : inequalities [#permalink]

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New post 05 Jun 2009, 04:20
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tejal777 wrote:
I've absolutly no clue of how to approach this ques.Can anyone please explain each of the answer choices?I tried folowing the first post but somehow got lost inbetween.Appreciate the help.

E. 2<=3x+4<=6

Let me try tejal777

A. x^4>=1 There are 2 solutions to this equation x = 1 and x = -1. Now this will make two lines on graph from 0 to 1 and 0 to -1. So not a single segment. Hence incorrect.
B. x^3<=27 I lost on this one earlier :oops: . This will have one solution x = 3 but the line segment would not be finite as on number line it can extend upwards and downwards to any length. Hence incorrect.
C. x^2>=16 This will be same as A. x = 4, -4. Hence incorrect.
D. 2<=IxI<=5 Same as A and C. x > 2, -x < 2 or -x > 5, x < 5. Hence incorrect.
E. 2<=3x+4<=6. This only will have one segment with finite length -2/3<=x<=2/3. Hence correct.

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Re: PS : inequalities   [#permalink] 05 Jun 2009, 04:20
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