Solve for x
x\in (-4,0]
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2x\geq 0 x+4<0
For the quotient to be ≤0, one of the values 2x and x+4 has to be ≥0, the other has to be ≤0, and x+4 cannot be zero. Consider the case when 2x\geq 0 and x+4 is negative.
x\in \emptyset
This is false for any x.
2x\leq 0 x+4>0
Consider the case when 2x\leq 0 and x+4 is positive.
x\in (-4,0]
The solution satisfying both inequalities is x\in \left(-4,0\right].
x\in (-4,0]
The final solution is the union of the obtained solutions.
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