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6x+4z=y
Swap sides so that all variable terms are on the left hand side.
6x=y-4z
Subtract 4z from both sides.
\frac{6x}{6}=\frac{y-4z}{6}
Divide both sides by 6.
x=\frac{y-4z}{6}
Dividing by 6 undoes the multiplication by 6.
x=\frac{y}{6}-\frac{2z}{3}
Divide y-4z by 6.