Solve for x
x\in (\frac{2}{5},\frac{8}{3}]
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\frac{3x-8}{50x-20}\leq 0
Use the distributive property to multiply 10 by 5x-2.
3x-8\geq 0 50x-20<0
For the quotient to be ≤0, one of the values 3x-8 and 50x-20 has to be ≥0, the other has to be ≤0, and 50x-20 cannot be zero. Consider the case when 3x-8\geq 0 and 50x-20 is negative.
x\in \emptyset
This is false for any x.
3x-8\leq 0 50x-20>0
Consider the case when 3x-8\leq 0 and 50x-20 is positive.
x\in (\frac{2}{5},\frac{8}{3}]
The solution satisfying both inequalities is x\in \left(\frac{2}{5},\frac{8}{3}\right].
x\in (\frac{2}{5},\frac{8}{3}]
The final solution is the union of the obtained solutions.
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