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\frac{1}{3}x+\frac{1}{3}\left(-6\right)-\frac{1}{3}x=x-2
Use the distributive property to multiply \frac{1}{3} by x-6.
\frac{1}{3}x+\frac{-6}{3}-\frac{1}{3}x=x-2
Multiply \frac{1}{3} and -6 to get \frac{-6}{3}.
\frac{1}{3}x-2-\frac{1}{3}x=x-2
Divide -6 by 3 to get -2.
-2=x-2
Combine \frac{1}{3}x and -\frac{1}{3}x to get 0.
x-2=-2
Swap sides so that all variable terms are on the left hand side.
x=-2+2
Add 2 to both sides.
x=0
Add -2 and 2 to get 0.