x is not 1, (1-x^5)/(1-x) < 1/1-x ?
(1) x>0
(2) x<1
using (1-x^5)/(1-x) < 1/1-x)
we can arrange the equation to be (1/1-x)- (x^5/1-x) <1/1-x
then rearrange again and get -x^5/1-x <0
multiplying each side by (1-x)^2 since its positive
=> -x^5(1-x) which is also x^5*(x-1)<0
dividing each side by x^4, we get x(x-1)<0, or 0<x<1 so the answer must be c
but what if from -x^5/(1-x)<0, instead of making it into x^5*(x-1)<0,
can u just take -x^5/(1-x)<0 and switch it to x^5/(1-x)>0 (taking out the negative sign?
for some reason if i do it that way my answer comes out differently..
(the answer is C btw)
-x^5/(1-x)<0, so is it legal to do this?
==> x^5/(1-x)>0
so is there a difference between x^5/(1-x)>0
and x^5*(x-1)<0 ?
my answer comes out different when i multiply each side by a negative (x^5/(1-x)>0 )
inequality question
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- Newbie | Next Rank: 10 Posts
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x is not 1, (1-x^5)/(1-x) < 1/1-x ?
(1) x>0
(2) x<1
cross multiply = (1-x^5)* (1-x) < 1-x
1-x-x^5 +x^6 < 1-x
Is x^5+x^6<0 ?
(1) x>0
Sufficient
2) x<1
Not Sufficient
x could be -1, where result = 0
x could be -2, where result >0
(1) x>0
(2) x<1
cross multiply = (1-x^5)* (1-x) < 1-x
1-x-x^5 +x^6 < 1-x
Is x^5+x^6<0 ?
(1) x>0
Sufficient
2) x<1
Not Sufficient
x could be -1, where result = 0
x could be -2, where result >0
GOOD LUCK ALL!
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- Junior | Next Rank: 30 Posts
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- Joined: Sat Jun 09, 2007 11:57 am
Did you say the answer was (C)?
If you back solve the answer it might be easier
1). says x>0, so plug in 1 to the equation
(1-1^5)/1-1 < 1/(1-1)
= 0 < 1/0 insuffient
2). says x<1, so plug in 0
(1-0^5)/1-0 < 1/(1-0)
= 1<1 insuffient
Together they say that x is between 0 and 1
If you plug in 1/2 into the equation it is sufficient.
If you back solve the answer it might be easier
1). says x>0, so plug in 1 to the equation
(1-1^5)/1-1 < 1/(1-1)
= 0 < 1/0 insuffient
2). says x<1, so plug in 0
(1-0^5)/1-0 < 1/(1-0)
= 1<1 insuffient
Together they say that x is between 0 and 1
If you plug in 1/2 into the equation it is sufficient.