Hello,
This question has been talked about before on this forum, but I don't understand why my method isn't working:
Is x negative?
(1) x^3(1-x^2)<0
(2) x^2-1<0
1) Distribute the exponent:
X^3-X^5<0
Move the terms to opposite sides of the equation
X^3<X^5
Test numbers:
If X >1 (i.e. X=2, X^3=8, X^5=32) -- stays true to given equation
If 0>X>-1 (i.e. X= -1/2, X^3= -1/8, X^5= -1/32) -- does not work with given equation, since X^3>X^5
Thus... this statement is SUFFICIENT, because only positive numbers work...
The O.G. says that any positive number greater than 1 will work, as will any negative number between 0 and -1. But I just proved that any number between 0 and -1 does not stay true to the given equation. What's wrong with the way I approached this question?
This question has been talked about before on this forum, but I don't understand why my method isn't working:
Is x negative?
(1) x^3(1-x^2)<0
(2) x^2-1<0
1) Distribute the exponent:
X^3-X^5<0
Move the terms to opposite sides of the equation
X^3<X^5
Test numbers:
If X >1 (i.e. X=2, X^3=8, X^5=32) -- stays true to given equation
If 0>X>-1 (i.e. X= -1/2, X^3= -1/8, X^5= -1/32) -- does not work with given equation, since X^3>X^5
Thus... this statement is SUFFICIENT, because only positive numbers work...
The O.G. says that any positive number greater than 1 will work, as will any negative number between 0 and -1. But I just proved that any number between 0 and -1 does not stay true to the given equation. What's wrong with the way I approached this question?
