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4x+1=2y
Swap sides so that all variable terms are on the left hand side.
4x=2y-1
Subtract 1 from both sides.
\frac{4x}{4}=\frac{2y-1}{4}
Divide both sides by 4.
x=\frac{2y-1}{4}
Dividing by 4 undoes the multiplication by 4.
x=\frac{y}{2}-\frac{1}{4}
Divide 2y-1 by 4.