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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the solution set of (1+|x|)(1+x) > 0? tagged by: Max@Math Revolution ##### This topic has 3 expert replies and 0 member replies ### GMAT/MBA Expert ## What is the solution set of (1+|x|)(1+x) > 0? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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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.

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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.

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

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