Solve varepsilon-xz-x=R

$$\varepsilon - x z - x = R$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\epsilon -R}{z+1}\text{, }&z\neq -1\\x\in \mathrm{R}\text{, }&\epsilon =R\text{ and }z=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \epsilon from both sides.

$$-xz-x=R-\epsilon$$

Combine all terms containing x.

$$\left(-z-1\right)x=R-\epsilon$$

Divide both sides by -z-1.

$$\frac{\left(-z-1\right)x}{-z-1}=\frac{R-\epsilon }{-z-1}$$

Dividing by -z-1 undoes the multiplication by -z-1.

$$x=\frac{R-\epsilon }{-z-1}$$

Divide R-\epsilon by -z-1.

$$x=-\frac{R-\epsilon }{z+1}$$

Solve for R

$$R=\epsilon -x-xz$$

Solution Steps

Swap sides so that all variable terms are on the left hand side.

$$R=\epsilon -xz-x$$