Solve for x
x\in (-3,1]
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1-x\leq 0 x+3<0
For the quotient to be ≥0, 1-x and x+3 have to be both ≤0 or both ≥0, and x+3 cannot be zero. Consider the case when 1-x\leq 0 and x+3 is negative.
x\in \emptyset
This is false for any x.
1-x\geq 0 x+3>0
Consider the case when 1-x\geq 0 and x+3 is positive.
x\in (-3,1]
The solution satisfying both inequalities is x\in \left(-3,1\right].
x\in (-3,1]
The final solution is the union of the obtained solutions.
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