Consider the equation rx-sx+y=z; solve for x

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So you just rewrite the equation to be equal to x so you need x on a side by itself.

rx-sx+y=z

First, subtract y.

rx-sx=z-y

Second, factor out the x.

x (r-s) = z-y

Lastly, divide (r-s) on both sides.

x = (z-y) / (r-s)