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x=\frac{1}{2}y-3
Divide each term of y-6 by 2 to get \frac{1}{2}y-3.
\frac{1}{2}y-3=x
Swap sides so that all variable terms are on the left hand side.
\frac{1}{2}y=x+3
Add 3 to both sides.
\frac{\frac{1}{2}y}{\frac{1}{2}}=\frac{x+3}{\frac{1}{2}}
Multiply both sides by 2.
y=\frac{x+3}{\frac{1}{2}}
Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.
y=2x+6
Divide x+3 by \frac{1}{2} by multiplying x+3 by the reciprocal of \frac{1}{2}.
x=\frac{1}{2}y-3
Divide each term of y-6 by 2 to get \frac{1}{2}y-3.