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

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

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New post 21 Nov 2016, 02:05
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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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Re: Which of the following inequalities satisfy (x-4) (x+1) >0?  [#permalink]

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New post 21 Nov 2016, 02:43
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
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Re: Which of the following inequalities satisfy (x-4) (x+1) >0?  [#permalink]

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New post 23 Nov 2016, 01:20
==> 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
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Re: Which of the following inequalities satisfy (x-4) (x+1) >0?  [#permalink]

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New post 24 Nov 2016, 20:14
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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New post 24 Nov 2016, 20:24
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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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New post 24 Nov 2016, 20:39
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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