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\frac{5}{6}\times \frac{1}{2}x+\frac{5}{6}\times 6-3x
Use the distributive property to multiply \frac{5}{6} by \frac{1}{2}x+6.
\frac{5\times 1}{6\times 2}x+\frac{5}{6}\times 6-3x
Multiply \frac{5}{6} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{5}{12}x+\frac{5}{6}\times 6-3x
Do the multiplications in the fraction \frac{5\times 1}{6\times 2}.
\frac{5}{12}x+5-3x
Cancel out 6 and 6.
-\frac{31}{12}x+5
Combine \frac{5}{12}x and -3x to get -\frac{31}{12}x.
\frac{5}{6}\times \frac{1}{2}x+\frac{5}{6}\times 6-3x
Use the distributive property to multiply \frac{5}{6} by \frac{1}{2}x+6.
\frac{5\times 1}{6\times 2}x+\frac{5}{6}\times 6-3x
Multiply \frac{5}{6} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{5}{12}x+\frac{5}{6}\times 6-3x
Do the multiplications in the fraction \frac{5\times 1}{6\times 2}.
\frac{5}{12}x+5-3x
Cancel out 6 and 6.
-\frac{31}{12}x+5
Combine \frac{5}{12}x and -3x to get -\frac{31}{12}x.