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21 Nov 2016, 02:05
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C
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Difficulty:
35%
(medium)
Question Stats:
71% (01:25) correct
29%
(01:44)
wrong
based on 266
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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
A. -1<x<4 B. -4<x<1 C. x<-1, 4<x D. x<-4, 1<x E. -1<x<1
21 Nov 2016, 02:43
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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
23 Nov 2016, 01:20
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==> 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
Answer: C
