(x —1)(x + 3) > 0
(x +5)(x—4) < 0
Which of the following values of x satisfy both inequalities shown?
A. I and II only
B. I and III only
C. II and III only
D. II and IV only
E. I, II, III, and IV
(x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.
Among choices only -4 and 2 satisfy both inequalities.
What is the underlying concept to solve these types of inequalities ? When (x - 1)(x + 3) > 0 , we can assume that either both entities are negative or positive. You seem to have assumed both x-1 and x +3 to be positive. Please do let me know where I'm going wrong in in analysing your solution.