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