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\frac{1}{6}x+11-\frac{2}{3}x=0
Subtract \frac{2}{3}x from both sides.
-\frac{1}{2}x+11=0
Combine \frac{1}{6}x and -\frac{2}{3}x to get -\frac{1}{2}x.
-\frac{1}{2}x=-11
Subtract 11 from both sides. Anything subtracted from zero gives its negation.
x=-11\left(-2\right)
Multiply both sides by -2, the reciprocal of -\frac{1}{2}.
x=22
Multiply -11 and -2 to get 22.