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x-8\geq \frac{14}{-7}
Divide both sides by -7. Since -7 is negative, the inequality direction is changed.
x-8\geq -2
Divide 14 by -7 to get -2.
x\geq -2+8
Add 8 to both sides.
x\geq 6
Add -2 and 8 to get 6.