Solve for x
x\in \left(-\infty,-3\right)\cup \left(3,\infty\right)
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2x+6>0 3-x<0
For the product to be negative, 2x+6 and 3-x have to be of the opposite signs. Consider the case when 2x+6 is positive and 3-x is negative.
x>3
The solution satisfying both inequalities is x>3.
3-x>0 2x+6<0
Consider the case when 3-x is positive and 2x+6 is negative.
x<-3
The solution satisfying both inequalities is x<-3.
x>3\text{; }x<-3
The final solution is the union of the obtained solutions.
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