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