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\frac{1}{2}x-\frac{1}{3}x>0
Subtract \frac{1}{3}x from both sides.
\frac{1}{6}x>0
Combine \frac{1}{2}x and -\frac{1}{3}x to get \frac{1}{6}x.
x>0
Product of two numbers is >0 if both are >0 or both are <0. Since \frac{1}{6}>0, x must be >0.