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How many integers $n$ satisfy $(n-2)(n+4)<0$?

 Mar 2, 2018
 #1
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(n - 2) (n + 4)  < 0

 

If we solved this

 

(n - 2) ( n + 4)  = 0

 

The solutions would be  n  = 2  and n  =  -4

 

So......the solutions to  the inequality lie on the possible intervals

 

(-inf, - 4) , ( -4, 2)  ,  (2, inf )

 

Testing  n  =  0  in the middle interval   will make the inequality true, while the outside two intervals don't 

 

So...the solution is  (-4, 2)   ....and  5 integers lie in this interval

 

 

cool cool cool

 Mar 2, 2018

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