Solve for x
x\in \left(-3,3\right)
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x-3>0 2x+6<0
For the quotient to be negative, x-3 and 2x+6 have to be of the opposite signs. Consider the case when x-3 is positive and 2x+6 is negative.
x\in \emptyset
This is false for any x.
2x+6>0 x-3<0
Consider the case when 2x+6 is positive and x-3 is negative.
x\in \left(-3,3\right)
The solution satisfying both inequalities is x\in \left(-3,3\right).
x\in \left(-3,3\right)
The final solution is the union of the obtained solutions.
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