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\frac{-96}{8}\leq x-6
Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.
-12\leq x-6
Divide -96 by 8 to get -12.
x-6\geq -12
Swap sides so that all variable terms are on the left hand side. This changes the sign direction.
x\geq -12+6
Add 6 to both sides.
x\geq -6
Add -12 and 6 to get -6.