Inequalities

[moneyman]

Is x+1/x-3 <0??

(1)-1<x<1
(2)x^2 - 4<0

[samirpandeyit62]

Is x+1/x-3 <0??

(1)-1<x<1

here x+1 will always be +ve coz x can assume max -ve value of -.99..

& x-3 will always be -ve coz max +ve that x can assume is .99..

hence the expr will be -ve & < 0 SUFF

(2)x^2 - 4<0

here x^ 2 will be +ve & X^2 can assume a max value less than 4 but x can be both +ve as well as -ve e.g. 1.5 or -1.5

say if x =1.5 then x+1/x-3 <0 but if x =-1.5 then x+1/x-3 will be +ve & > 0
Hence INSUFF

A

[agni_mba]

good one samir.

alternatively if you solve x+1/x-3 <0, you will get -1<x<3

1's equation's solution means x should fall in between [-1,1], therefore it satisfies.

2 equation's solution means x should fall in between [-2,2], and that range doesn't fall in the solution range of the given equation. Hence A is the answer.

[gmatrant]

good one samir.

alternatively if you solve x+1/x-3 <0, you will get -1<x<3

1's equation's solution means x should fall in between [-1,1], therefore it satisfies.

2 equation's solution means x should fall in between [-2,2], and that range doesn't fall in the solution range of the given equation. Hence A is the answer.

I have an inequality paranoia!

from your quote if you solve x+1/x-3 <0, you will get -1<x<3

well this is how i tried to solve
multiple both side with (x-3)
so you get (x+1)(x-3)<0
so x <-1 and x<3
so how did -1<x<3 happen.. im sure ive missed something very naive.. can you pls explain

Also i have another doubt if I say x<-1 can it also mean x>1..

[ri2007]

good one samir.

alternatively if you solve x+1/x-3 <0, you will get -1<x<3

1's equation's solution means x should fall in between [-1,1], therefore it satisfies.

2 equation's solution means x should fall in between [-2,2], and that range doesn't fall in the solution range of the given equation. Hence A is the answer.

I have an inequality paranoia!

from your quote if you solve x+1/x-3 <0, you will get -1<x<3

well this is how i tried to solve
multiple both side with (x-3)
so you get (x+1)(x-3)<0
so x <-1 and x<3
so how did -1<x<3 happen.. im sure ive missed something very naive.. can you pls explain

Also i have another doubt if I say x<-1 can it also mean x>1..

Hi

you have made a small mistake aboove.

multiple both side with (x-3)
you do not get (x+1)(x-3)<0
you get (x+1)<0

but any way I feel u should look at the question and decide how to best solve it. I myself am really bad with number properties and inrqualities, but the more question I look at the better I get. And this forum is great with people helping out all the time. So should be ok, I hope))