Question

solve: (x+2)(x-11)(x+1)>0

Answer 1

critical values: x = -2, -1, and 11

pick any number <-2, say x=-5
(-)(-)(-) > 0 ? NO
pick any number between -2 and -1, say x = -1.5
(+)(-)(-) > 0 ? YES
pick any number between -1 and 11 , say x=0
(+)(-)(=) > 0 ? , NO
pick any number > 11 , say x=20
(+)(+)(+) > 0 ?, YES

so
-2 < x < -1 OR x > 11

OR

look at the graph of y = (x+2)(x-11)(x+1)
and the above solution is obvious.