Solve for x
x\in [\frac{165}{7},35)
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7x-165\geq 0 x-35<0
For the quotient to be ≤0, one of the values 7x-165 and x-35 has to be ≥0, the other has to be ≤0, and x-35 cannot be zero. Consider the case when 7x-165\geq 0 and x-35 is negative.
x\in [\frac{165}{7},35)
The solution satisfying both inequalities is x\in \left[\frac{165}{7},35\right).
7x-165\leq 0 x-35>0
Consider the case when 7x-165\leq 0 and x-35 is positive.
x\in \emptyset
This is false for any x.
x\in [\frac{165}{7},35)
The final solution is the union of the obtained solutions.
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