Solve for x
x\in (-\infty,-2]\cup (7,\infty)
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x+2\leq 0 x-7<0
For the quotient to be ≥0, x+2 and x-7 have to be both ≤0 or both ≥0, and x-7 cannot be zero. Consider the case when x+2\leq 0 and x-7 is negative.
x\leq -2
The solution satisfying both inequalities is x\leq -2.
x+2\geq 0 x-7>0
Consider the case when x+2\geq 0 and x-7 is positive.
x>7
The solution satisfying both inequalities is x>7.
x\leq -2\text{; }x>7
The final solution is the union of the obtained solutions.
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