Solve for r E=V+Ir

$E = V + I r$

Step 1

Rewrite the equation as $V + I r = E$ .

$V + I r = E$

Step 2

Subtract $V$ from both sides of the equation.

$I r = E - V$

Step 3

Divide each term in $I r = E - V$ by $I$ and simplify.

Divide each term in $I r = E - V$ by $I$ .

$\frac{I r}{I} = \frac{E}{I} + \frac{- V}{I}$

Simplify the left side.

Cancel the common factor of $I$ .

Cancel the common factor.

$\frac{I r}{I} = \frac{E}{I} + \frac{- V}{I}$

Divide $r$ by $1$ .

$r = \frac{E}{I} + \frac{- V}{I}$

Simplify the right side.

Move the negative in front of the fraction.

$r = \frac{E}{I} - \frac{V}{I}$