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-\frac{5}{6}x-10=y
Swap sides so that all variable terms are on the left hand side.
-\frac{5}{6}x=y+10
Add 10 to both sides.
\frac{-\frac{5}{6}x}{-\frac{5}{6}}=\frac{y+10}{-\frac{5}{6}}
Divide both sides of the equation by -\frac{5}{6}, which is the same as multiplying both sides by the reciprocal of the fraction.
x=\frac{y+10}{-\frac{5}{6}}
Dividing by -\frac{5}{6} undoes the multiplication by -\frac{5}{6}.
x=-\frac{6y}{5}-12
Divide y+10 by -\frac{5}{6} by multiplying y+10 by the reciprocal of -\frac{5}{6}.