SOLUTION: If x is a negative number, which of the following must be true? I) x^5 < |x| II) x < &#8730;(-x) III) x - 1/|x| < 0 A) I, II and III B) I and II only C) None D) II

Algebra ->  Signed-numbers -> SOLUTION: If x is a negative number, which of the following must be true? I) x^5 < |x| II) x < &#8730;(-x) III) x - 1/|x| < 0 A) I, II and III B) I and II only C) None D) II       Log On


   

Question 304975: If x is a negative number, which of the following must be true?
I) x^5 < |x|
II) x < √(-x)
III) x - 1/|x| < 0
A) I, II and III
B) I and II only
C) None
D) II and III only
E) I and III only
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
x < 0 ----> x^5 < 0

I) x^5 < 0 < |x| ----> true
II) x < 0 < sqrt(-x) ----> true
III) x - 1/|x| = (negative) - (positive) = negative < 0 ----> true

A) I, II, and III are true.