Solve for x
x\in (-2,7]
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7-x\leq 0 3x+6<0
For the quotient to be ≥0, 7-x and 3x+6 have to be both ≤0 or both ≥0, and 3x+6 cannot be zero. Consider the case when 7-x\leq 0 and 3x+6 is negative.
x\in \emptyset
This is false for any x.
7-x\geq 0 3x+6>0
Consider the case when 7-x\geq 0 and 3x+6 is positive.
x\in (-2,7]
The solution satisfying both inequalities is x\in \left(-2,7\right].
x\in (-2,7]
The final solution is the union of the obtained solutions.
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