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\frac{1}{2}x+\frac{3}{2}x>4
Add \frac{3}{2}x to both sides.
2x>4
Combine \frac{1}{2}x and \frac{3}{2}x to get 2x.
x>\frac{4}{2}
Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.
x>2
Divide 4 by 2 to get 2.