Solve for x
x\in (-\infty,2]\cup (5,\infty)
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x-2\leq 0 2x-10<0
For the quotient to be ≥0, x-2 and 2x-10 have to be both ≤0 or both ≥0, and 2x-10 cannot be zero. Consider the case when x-2\leq 0 and 2x-10 is negative.
x\leq 2
The solution satisfying both inequalities is x\leq 2.
x-2\geq 0 2x-10>0
Consider the case when x-2\geq 0 and 2x-10 is positive.
x>5
The solution satisfying both inequalities is x>5.
x\leq 2\text{; }x>5
The final solution is the union of the obtained solutions.
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