Solve for x
x\in (-2,0]
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x\geq 0 5x+10<0
For the quotient to be ≤0, one of the values x and 5x+10 has to be ≥0, the other has to be ≤0, and 5x+10 cannot be zero. Consider the case when x\geq 0 and 5x+10 is negative.
x\in \emptyset
This is false for any x.
x\leq 0 5x+10>0
Consider the case when x\leq 0 and 5x+10 is positive.
x\in (-2,0]
The solution satisfying both inequalities is x\in \left(-2,0\right].
x\in (-2,0]
The final solution is the union of the obtained solutions.
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