Answer:
The conjecture cannot work for any negative numbers, It works for x > 1.3.
Step-by-step explanation:
An odd power preserves the sign. For |x| > 1, the power increases the magnitude. For x < 0, adding -2 only increases the magnitude more. A negative number of larger magnitude will not be "greater than" the reference. It will be "less than."
It only takes a counterexample to show the conjecture is incorrect.
x^5 -2 ?? x
(-2)^5 -2 ?? (-2)
-32 -2 ?? -2
-34 < -2 . . . . . . not greater than
