Marcab wrote:
If \(x\neq{0}\) and \(\frac{x}{|x|}<x\), which of the following must be true?
(A) \(x>1\)
(B) \(x>-1\)
(C) \(|x|<1\)
(D) \(|x|>1\)
(E) \(-1<x<0\)
We can simplify the given inequality:
x/|x| < x
x < (x)|x|
(x)|x| > x
If x is positive, we can divide both sides by x and obtain |x| > 1.
If x is negative, we can also divide both sides by x, but we have to switch the inequality sign, so we have |x| < 1.
We see that if x is positive, |x| > 1, which is choice C, and if x is negative,
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