Skywalker18 wrote:
If |x| < x^2, which of the following must be true ?
A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1
It's possible that x=2, since \(|2| < 2^2\).
Eliminate B and D, since they do not have to be true.
It's possible that x=-2, since \(|-2| < (-2)^2\).
Eliminate A and C, since they do not have to be true.
Algebra:
\(|x| < x^2\)
\(|x| < |x| * |x|\)Since |x| in the blue inequality must be NONNEGATIVE, we can safely divide each side by |x|:
\(\frac{|x|}{|x|} < |x| * \frac{|x|}{|x|}\)
\(1 < |x|\)Since each side of the red inequality is NONNEGATIVE, we can safely square each side:
\(1^2 < |x|^2\)
\(1 < x^2\)
\(x^2 > 1\)
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