Solve for x
x\in [\frac{2}{5},\frac{1}{2})
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\frac{-5x+1+1}{2x-1}\geq 0
Combine -3x and -2x to get -5x.
\frac{-5x+2}{2x-1}\geq 0
Add 1 and 1 to get 2.
2-5x\leq 0 2x-1<0
For the quotient to be ≥0, 2-5x and 2x-1 have to be both ≤0 or both ≥0, and 2x-1 cannot be zero. Consider the case when 2-5x\leq 0 and 2x-1 is negative.
x\in [\frac{2}{5},\frac{1}{2})
The solution satisfying both inequalities is x\in \left[\frac{2}{5},\frac{1}{2}\right).
2-5x\geq 0 2x-1>0
Consider the case when 2-5x\geq 0 and 2x-1 is positive.
x\in \emptyset
This is false for any x.
x\in [\frac{2}{5},\frac{1}{2})
The final solution is the union of the obtained solutions.
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