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\frac{2}{3}x+4-\frac{1}{2}x=6
Subtract \frac{1}{2}x from both sides.
\frac{1}{6}x+4=6
Combine \frac{2}{3}x and -\frac{1}{2}x to get \frac{1}{6}x.
\frac{1}{6}x=6-4
Subtract 4 from both sides.
\frac{1}{6}x=2
Subtract 4 from 6 to get 2.
x=2\times 6
Multiply both sides by 6, the reciprocal of \frac{1}{6}.
x=12
Multiply 2 and 6 to get 12.