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\frac{1}{3}x+12-x=0
Subtract x from both sides.
-\frac{2}{3}x+12=0
Combine \frac{1}{3}x and -x to get -\frac{2}{3}x.
-\frac{2}{3}x=-12
Subtract 12 from both sides. Anything subtracted from zero gives its negation.
x=-12\left(-\frac{3}{2}\right)
Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.
x=\frac{-12\left(-3\right)}{2}
Express -12\left(-\frac{3}{2}\right) as a single fraction.
x=\frac{36}{2}
Multiply -12 and -3 to get 36.
x=18
Divide 36 by 2 to get 18.