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5z-6-7z\geq 1
Subtract 7z from both sides.
-2z-6\geq 1
Combine 5z and -7z to get -2z.
-2z\geq 1+6
Add 6 to both sides.
-2z\geq 7
Add 1 and 6 to get 7.
z\leq -\frac{7}{2}
Divide both sides by -2. Since -2 is negative, the inequality direction is changed.