Solve for x
x\in (-6,5]
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x-5\geq 0 x+6<0
For the quotient to be ≤0, one of the values x-5 and x+6 has to be ≥0, the other has to be ≤0, and x+6 cannot be zero. Consider the case when x-5\geq 0 and x+6 is negative.
x\in \emptyset
This is false for any x.
x-5\leq 0 x+6>0
Consider the case when x-5\leq 0 and x+6 is positive.
x\in (-6,5]
The solution satisfying both inequalities is x\in \left(-6,5\right].
x\in (-6,5]
The final solution is the union of the obtained solutions.
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