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\frac{2}{3}x-\frac{5}{6}x<0
Subtract \frac{5}{6}x from both sides.
-\frac{1}{6}x<0
Combine \frac{2}{3}x and -\frac{5}{6}x to get -\frac{1}{6}x.
x>0
Product of two numbers is <0 if one is >0 and the other is <0. Since -\frac{1}{6}<0, x must be >0.