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\frac{1}{2}x+8-\frac{5}{6}x=0
Subtract \frac{5}{6}x from both sides.
-\frac{1}{3}x+8=0
Combine \frac{1}{2}x and -\frac{5}{6}x to get -\frac{1}{3}x.
-\frac{1}{3}x=-8
Subtract 8 from both sides. Anything subtracted from zero gives its negation.
x=-8\left(-3\right)
Multiply both sides by -3, the reciprocal of -\frac{1}{3}.
x=24
Multiply -8 and -3 to get 24.