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y=\frac{1}{2}x-\frac{1}{2}
Divide each term of x-1 by 2 to get \frac{1}{2}x-\frac{1}{2}.
\frac{1}{2}x-\frac{1}{2}=y
Swap sides so that all variable terms are on the left hand side.
\frac{1}{2}x=y+\frac{1}{2}
Add \frac{1}{2} to both sides.
\frac{\frac{1}{2}x}{\frac{1}{2}}=\frac{y+\frac{1}{2}}{\frac{1}{2}}
Multiply both sides by 2.
x=\frac{y+\frac{1}{2}}{\frac{1}{2}}
Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.
x=2y+1
Divide y+\frac{1}{2} by \frac{1}{2} by multiplying y+\frac{1}{2} by the reciprocal of \frac{1}{2}.
y=\frac{1}{2}x-\frac{1}{2}
Divide each term of x-1 by 2 to get \frac{1}{2}x-\frac{1}{2}.