Solve for x
x\in [-2,5)
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2x+4\leq 0 5-x<0
For the quotient to be ≥0, 2x+4 and 5-x have to be both ≤0 or both ≥0, and 5-x cannot be zero. Consider the case when 2x+4\leq 0 and 5-x is negative.
x\in \emptyset
This is false for any x.
2x+4\geq 0 5-x>0
Consider the case when 2x+4\geq 0 and 5-x is positive.
x\in [-2,5)
The solution satisfying both inequalities is x\in \left[-2,5\right).
x\in [-2,5)
The final solution is the union of the obtained solutions.
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