Solve for x
x\in \left(-\infty,-1\right)\cup \left(2,\infty\right)
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x+1>0 2-x<0
For the product to be negative, x+1 and 2-x have to be of the opposite signs. Consider the case when x+1 is positive and 2-x is negative.
x>2
The solution satisfying both inequalities is x>2.
2-x>0 x+1<0
Consider the case when 2-x is positive and x+1 is negative.
x<-1
The solution satisfying both inequalities is x<-1.
x>2\text{; }x<-1
The final solution is the union of the obtained solutions.
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