The given Inequality is (x+1)(x-3)(x+2)(x-4)<0

The critical points are x=-2, x=-1, x=3 and x=4. We can test for the validity of the inequality in the intervals (-∞, -2) , (-2, -1), (-1,3) , (3,4) and (4, ∞). We can now use Test point method to work out the solution to the given inequality, as follows

Interval Test point Inequality value

(in the interval)

(-∞, -2) -3 (-2)(-6)(-1)(-7)= 84

(-2,-1) -3/2 (-1/2)(-7/2)(1/2)(-11/2)=-77/16

(-1,3) 0 (1)(-3)(2)(-4) =24

(3,4) 7/2 (9/2)(1/2)(11/2)(-1/2)=-99/8

(4,∞) 9/2 (11/2)(3/2)(13/2)(1/2)=143/8

It is seen from the above that inequality holds good in the open intervals (-2,-1) and (3,4). Hence the solution to the inequality will be -2<x<-1 and 3<x<4.