Solve for x
x\in (-\infty,-\frac{5}{2})\cup [6,\infty)
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2x-12\leq 0 2x+5<0
For the quotient to be ≥0, 2x-12 and 2x+5 have to be both ≤0 or both ≥0, and 2x+5 cannot be zero. Consider the case when 2x-12\leq 0 and 2x+5 is negative.
x<-\frac{5}{2}
The solution satisfying both inequalities is x<-\frac{5}{2}.
2x-12\geq 0 2x+5>0
Consider the case when 2x-12\geq 0 and 2x+5 is positive.
x\geq 6
The solution satisfying both inequalities is x\geq 6.
x<-\frac{5}{2}\text{; }x\geq 6
The final solution is the union of the obtained solutions.
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