Solve for x
x\in (0,1]
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1-x\leq 0 2x<0
For the quotient to be ≥0, 1-x and 2x have to be both ≤0 or both ≥0, and 2x cannot be zero. Consider the case when 1-x\leq 0 and 2x is negative.
x\in \emptyset
This is false for any x.
1-x\geq 0 2x>0
Consider the case when 1-x\geq 0 and 2x is positive.
x\in (0,1]
The solution satisfying both inequalities is x\in \left(0,1\right].
x\in (0,1]
The final solution is the union of the obtained solutions.
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