Solve i=E/R+frac{r{2}}

$$i = \frac { E } { R + \frac { r } { 2 } }$$

Solve for E

$$E=\frac{ir}{2}+iR$$

$$R\neq -\frac{r}{2}$$

Steps for Solving Linear Equation

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

$$\frac{E}{R+\frac{r}{2}}=i$$

The equation is in standard form.

$$\frac{1}{\frac{r}{2}+R}E=i$$

Divide both sides by \left(R+\frac{1}{2}r\right)^{-1}.

$$\frac{\frac{1}{\frac{r}{2}+R}E\left(\frac{r}{2}+R\right)}{1}=\frac{i\left(\frac{r}{2}+R\right)}{1}$$

Dividing by \left(R+\frac{1}{2}r\right)^{-1} undoes the multiplication by \left(R+\frac{1}{2}r\right)^{-1}.

$$E=\frac{i\left(\frac{r}{2}+R\right)}{1}$$

Divide i by \left(R+\frac{1}{2}r\right)^{-1}.

$$E=\frac{ir}{2}+iR$$

Solve for R

$$R=-\frac{r}{2}-iE$$

$$E\neq 0$$