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# Which of the following inequalities satisfy (x-4) (x+1) >0?

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Math Revolution GMAT Instructor
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Which of the following inequalities satisfy (x-4) (x+1) >0?  [#permalink]

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21 Nov 2016, 01:05
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25% (medium)

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69% (01:24) correct 31% (01:40) wrong based on 137 sessions

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Which of the following inequalities satisfy (x-4) (x+1) >0?

A. -1<x<4 B. -4<x<1 C. x<-1, 4<x D. x<-4, 1<x E. -1<x<1

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior CR Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1366 Location: Viet Nam Re: Which of the following inequalities satisfy (x-4) (x+1) >0? [#permalink] ### Show Tags 21 Nov 2016, 01:43 MathRevolution wrote: Which of the following inequalities satisfy (x-4) (x+1) >0? A. -1<x<4 B. -4<x<1 C. x<-1, 4<x D. x<-4, 1<x E. -1<x<1 Solve for inequation $$(x-4) (x+1) >0$$ If $$x<-1$$, we have $$x-4<0$$ and $$x+1<0$$, so $$(x-4) (x+1) >0$$ If $$-1 \leq x \leq 4$$, we have $$x-4 \leq 0$$ and $$x+1 \geq 0$$, so $$(x-4) (x+1) \leq 0$$ If $$x > 4$$, we have $$x-4 > 0$$ and $$x+1 > 0$$, so $$(x-4) (x+1) >0$$ So the answer is $$x <-1$$ or $$x>4$$. The answer is C _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6966 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following inequalities satisfy (x-4) (x+1) >0? [#permalink] ### Show Tags 23 Nov 2016, 00:20 ==> From (x-4)(x+1)>0, you get x-4>0, x+1>0 or x-4<0, and x+1<0. Then, x-4>0 and x+1>0 is x>4 and x>-1, which becomes x>4, and x-4<0 and x+1<0 becomes x<-1 from x<4 and x<-1, hence the answer is x<-1 or 4<X. Therefore, the answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’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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Re: Which of the following inequalities satisfy (x-4) (x+1) >0?  [#permalink]

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24 Nov 2016, 19:14
Quote:
which becomes x>4, and x-4<0 and x+1<0 becomes x<-1 from x<4 and x<-1, hence the answer is x<-1 or 4<X. Therefore, the answer is C.

Could you please explain in further detail where you get "x-4<0 and x+1<0" from?
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Re: Which of the following inequalities satisfy (x-4) (x+1) >0?  [#permalink]

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24 Nov 2016, 19:24
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VS93 wrote:
Quote:
which becomes x>4, and x-4<0 and x+1<0 becomes x<-1 from x<4 and x<-1, hence the answer is x<-1 or 4<X. Therefore, the answer is C.

Could you please explain in further detail where you get "x-4<0 and x+1<0" from?

$$(x+4)(x-1)>0 \implies$$ $$\begin{case}x+4>0\\x-1>0\end{case}$$ or $$\begin{case} x+4 <0 \\ x-1<0 \end{case}$$
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Re: Which of the following inequalities satisfy (x-4) (x+1) >0?  [#permalink]

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24 Nov 2016, 19:39
Ok, because both terms on the left side can be either both positive or both negative! Thanks for the quick answer.
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Re: Which of the following inequalities satisfy (x-4) (x+1) >0?  [#permalink]

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06 Oct 2018, 12:11
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Re: Which of the following inequalities satisfy (x-4) (x+1) >0?   [#permalink] 06 Oct 2018, 12:11
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