Solve for x
x\in (-\infty,2)\cup [4,\infty)
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x-4\leq 0 3x-6<0
For the quotient to be ≥0, x-4 and 3x-6 have to be both ≤0 or both ≥0, and 3x-6 cannot be zero. Consider the case when x-4\leq 0 and 3x-6 is negative.
x<2
The solution satisfying both inequalities is x<2.
x-4\geq 0 3x-6>0
Consider the case when x-4\geq 0 and 3x-6 is positive.
x\geq 4
The solution satisfying both inequalities is x\geq 4.
x<2\text{; }x\geq 4
The final solution is the union of the obtained solutions.
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