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3x+7\geq 8
Swap sides so that all variable terms are on the left hand side. This changes the sign direction.
3x\geq 8-7
Subtract 7 from both sides.
3x\geq 1
Subtract 7 from 8 to get 1.
x\geq \frac{1}{3}
Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.