Solve for x
x\in \left(-\infty,-5\right)\cup \left(8,\infty\right)
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x+5>0 8-x<0
For the product to be negative, x+5 and 8-x have to be of the opposite signs. Consider the case when x+5 is positive and 8-x is negative.
x>8
The solution satisfying both inequalities is x>8.
8-x>0 x+5<0
Consider the case when 8-x is positive and x+5 is negative.
x<-5
The solution satisfying both inequalities is x<-5.
x>8\text{; }x<-5
The final solution is the union of the obtained solutions.
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