inequalities

A says

X^2>9
X^2-9>0
(X-3) ( X+3)> 0

for ineq to be positive

either both the terms should be less than 0 or both should be greater than 0.

X-3>, X+3>0 ; X-3<0 X+3<0
X>3 X>-3 ; X<3 X<-3

If X>3 then there no use of X>-3 and since X is negative so leave this

since X<-3 so leave X<3.. and this is what we wanted


B is crappy

X is less than cube root of -9 which it can take value greater and less than -3. eg. -2.1 to -2.9 and beyond -3

(1) x > 3 or x < -3, since we know x is negative, sufficient
(2) x < -9^(1/3) . approximately x < -2.1, insufficient

A

General question: if x>1, x<-1, and x<0 then is x<-1?? Coz i feel that it is true. please expalin if i am wrong.

Yes, if you divide an inequalities by a negative number the crocodile changes directions hence:

if X>1, then -X<-1

Yes, if you divide an inequalities by a negative number the crocodile changes directions hence:

if X>1, then -X<-1