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\frac{1}{2}x+1>3
Swap sides so that all variable terms are on the left hand side. This changes the sign direction.
\frac{1}{2}x>3-1
Subtract 1 from both sides.
\frac{1}{2}x>2
Subtract 1 from 3 to get 2.
x>2\times 2
Multiply both sides by 2, the reciprocal of \frac{1}{2}. Since \frac{1}{2} is positive, the inequality direction remains the same.
x>4
Multiply 2 and 2 to get 4.