Solve for x
x\in \left(-7,-2\right)
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-x-7<0 2x+4<0
For the quotient to be positive, -x-7 and 2x+4 have to be both negative or both positive. Consider the case when -x-7 and 2x+4 are both negative.
x\in \left(-7,-2\right)
The solution satisfying both inequalities is x\in \left(-7,-2\right).
2x+4>0 -x-7>0
Consider the case when -x-7 and 2x+4 are both positive.
x\in \emptyset
This is false for any x.
x\in \left(-7,-2\right)
The final solution is the union of the obtained solutions.
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