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# If |x| < x^2, which of the following must be true ?

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Joined: 04 Aug 2010
Posts: 273
Schools: Dartmouth College
Re: If |x| < x^2, which of the following must be true ?  [#permalink]

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28 Jun 2018, 10:21
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dave13 wrote:
hey GMATGuruNY great explanation ! i have just one question

Algebra:
$$|x| < x^2$$ (as you see $$x^2$$ is without bars / brackets )

$$|x| < |x| * |x|$$ Here you rewrite $$x^2$$as |x| * |x| and not as x*x , can you please explain why ?

many thanks !

$$x^2 = x * x = |x| * |x|$$

For example:
$$3^2 = 3 * 3 = |3| * |3| = 9$$
$$(-3)^2 = -3 * -3 = |-3| * |-3| = 9$$

Given inequality:
$$|x| < x^2$$

Here, I chose to replace x^2 with |x| * |x| so that |x| would appear on both sides, enabling me to divide both sides by |x|:
$$|x| < x^2$$
$$|x| < |x| * |x|$$
$$\frac{|x|}{|x|} < |x| * \frac{|x|}{|x|}$$
$$1 < |x|$$
$$|x| > 1$$
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Re: If |x| < x^2, which of the following must be true ? &nbs [#permalink] 28 Jun 2018, 10:21

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