IMO: -1/2

X^11-X^3>0

that will occur if X>1 or -1<X<0

To make question easier:
x^11 - x^3 > 0 = x^11>x^3

Therefore x > 1 or -1<x<0
Only possibility is (-1/2)

To further explain this:
Since Both terms are to an odd power (11 and 3), x can not be a negative number greater than 1 or the answer is negative.. If they were to an even power, the sign of the number would not matter because it would be the result would be positive.

Also, 1^(any power) will always equal one, so 1^11 - 1^3 = 0

Furthermore, when a fraction is an exponent, it gets smaller as the exponent get larger.

i.e.
(1/2)^2 = 1/4
(1/2)^3 = 1/6

Therefore if positive x is a fraction x^3 > x^11 thus creating a negative answer.


But if x is a negative fraction, x^11 will be greater than x^3, thus it must be positive

Answer: (-1/2)