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Solution of the inequality \:\left(x\:+\:1\right)\left(x\:-\:2\right)\left(x+7\right)\:<\:0 is

Option: 1

x\in(-7,-1)\cup(2,\infty)


Option: 2

x\in(-7,1)\cup(2,\infty)


Option: 3

x\in(-\infty,-7)\cup(-1,2)


Option: 4

x\in(-\infty,-7)\cup(1,2)


Answers (1)

best_answer

\\we \;have\;\:\left(x\:+\:1\right)\left(x\:-\:2\right)\left(x+7\right)\:<\:0\\on\;number\;line\;mark\;\;x=-1,2,-7

When x > 2, all factors,  (x + 1), (x - 2) and (x + 7) is positive

Now put positive and negative sign as shown in figure 

Hence answer  is x\in(-\infty,-7)\cup(-1,2)  

 

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Riya

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