Solve for x
x\in \left(-\infty,-4\right)\cup \left(6,\infty\right)
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2x+8>0 18-3x<0
For the quotient to be negative, 2x+8 and 18-3x have to be of the opposite signs. Consider the case when 2x+8 is positive and 18-3x is negative.
x>6
The solution satisfying both inequalities is x>6.
18-3x>0 2x+8<0
Consider the case when 18-3x is positive and 2x+8 is negative.
x<-4
The solution satisfying both inequalities is x<-4.
x>6\text{; }x<-4
The final solution is the union of the obtained solutions.
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