Question

How do you solve `(x-8)(x+3)>0`?

Answer 1

x>8 or x<-3
Interval notation `(-oo,-3)U(8,oo)`

Explanation:

This is a quadratic inequality. It would hold good if either both factors are >0 or both are <0

In the first case, when both are positive(>0), it would mean x>8 and x>-3. If x>8, then it would automatically be >-3. Hence if x>8, it would be a solution of the given inequality.

In the second case, when both are negative(<0), it would mean x<8 and x<-3. If x<-3, then it would automatically be <8. Hence if x<-3, it would be a solution of the given inequality.