Solve for x
x\in [0,2)
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\frac{4x}{3x-6}\leq 0
Combine 5x and -x to get 4x.
4x\geq 0 3x-6<0
For the quotient to be ≤0, one of the values 4x and 3x-6 has to be ≥0, the other has to be ≤0, and 3x-6 cannot be zero. Consider the case when 4x\geq 0 and 3x-6 is negative.
x\in [0,2)
The solution satisfying both inequalities is x\in \left[0,2\right).
4x\leq 0 3x-6>0
Consider the case when 4x\leq 0 and 3x-6 is positive.
x\in \emptyset
This is false for any x.
x\in [0,2)
The final solution is the union of the obtained solutions.
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