Solve the following inequality x 42 x 83 0Solutionx42x830

Solve the following inequality: (x - 4)^2 (x + 8)^3 > 0.

(x-4)^2(x+8)^3>0

Testing points

x-4=0,x+8=0

x=4,-8

Testing regions are(-infinity,-8),(-8,4),(4,infinity)

In first region ,the left side of the inequality is less than 0.

In second and third region it is greater than 0.

Hence the solution is (-8,4)U(4,infinity)