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What is the solution set of (1+|x|)(1+x) > 0?

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by Max@Math Revolution » Mon Dec 10, 2018 12:22 am

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[Math Revolution GMAT math practice question]

What is the solution set of (1+|x|)(1+x) > 0?

A. x > -1
B. x < -1
C. x < 0
D. x > 0
E. x > 1
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by GMATGuruNY » Mon Dec 10, 2018 3:29 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

What is the solution set of (1+|x|)(1+x) > 0?

A. x > -1
B. x < -1
C. x < 0
D. x > 0
E. x > 1
x=0 satisfies (1+|x|)(1+x) > 0.
Since x=0 is not included in B, C, D or E, eliminate B, C, D and E.

The correct answer is A.
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What is the solution set of (1+|x|)(1+x) > 0?

by fskilnik@GMATH » Mon Dec 10, 2018 3:54 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

What is the solution set of (1+|x|)(1+x) > 0?

A. x > -1
B. x < -1
C. x < 0
D. x > 0
E. x > 1
$$?\,\,\,:\,\,\,\left( {1 + \left| x \right|\,} \right)\left( {1 + x} \right) > 0\,\,\,{\rm{solution}}\,\,{\rm{set}}\,$$
$$1 + \left| x \right|\,\,\, \ge \,\,\,1\,\,\,\, \Rightarrow \,\,\,\,1 + \left| x \right| > 0\,\,\,\,\,\left( {{\rm{for}}\,\,{\rm{all}}\,\,x} \right)\,\,\,\,\,\left( * \right)$$
$$\left( {1 + \left| x \right|\,} \right)\left( {1 + x} \right) > 0\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,1 + x > 0\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x > - 1$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Max@Math Revolution » Wed Dec 12, 2018 1:17 am
=>

Since 1+|x| > 0, we can divide both sides of the inequality by 1 + |x| to obtain 1+x > 0 or x > -1.

Therefore, the answer is A.
Answer: A
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