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\frac{1}{6}x-7=y
Swap sides so that all variable terms are on the left hand side.
\frac{1}{6}x=y+7
Add 7 to both sides.
\frac{\frac{1}{6}x}{\frac{1}{6}}=\frac{y+7}{\frac{1}{6}}
Multiply both sides by 6.
x=\frac{y+7}{\frac{1}{6}}
Dividing by \frac{1}{6} undoes the multiplication by \frac{1}{6}.
x=6y+42
Divide y+7 by \frac{1}{6} by multiplying y+7 by the reciprocal of \frac{1}{6}.