Solve for x
x\in [-4,3)
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x+4\geq 0 x-3<0
For the quotient to be ≤0, one of the values x+4 and x-3 has to be ≥0, the other has to be ≤0, and x-3 cannot be zero. Consider the case when x+4\geq 0 and x-3 is negative.
x\in [-4,3)
The solution satisfying both inequalities is x\in \left[-4,3\right).
x+4\leq 0 x-3>0
Consider the case when x+4\leq 0 and x-3 is positive.
x\in \emptyset
This is false for any x.
x\in [-4,3)
The final solution is the union of the obtained solutions.
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