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\frac{4}{3}x+55=y
Swap sides so that all variable terms are on the left hand side.
\frac{4}{3}x=y-55
Subtract 55 from both sides.
\frac{\frac{4}{3}x}{\frac{4}{3}}=\frac{y-55}{\frac{4}{3}}
Divide both sides of the equation by \frac{4}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.
x=\frac{y-55}{\frac{4}{3}}
Dividing by \frac{4}{3} undoes the multiplication by \frac{4}{3}.
x=\frac{3y-165}{4}
Divide y-55 by \frac{4}{3} by multiplying y-55 by the reciprocal of \frac{4}{3}.