Solve for D f=-m+1/7rD

$f = - m + \frac{1}{7} r D$

Rewrite the equation as $- m + \frac{1}{7} \cdot (r D) = f$ .

$- m + \frac{1}{7} \cdot (r D) = f$

Multiply $\frac{1}{7} (r D)$ .

Combine $r$ and $\frac{1}{7}$ .

$- m + \frac{r}{7} D = f$

Combine $\frac{r}{7}$ and $D$ .

$- m + \frac{r D}{7} = f$

Add $m$ to both sides of the equation.

$\frac{r D}{7} = f + m$

Multiply both sides of the equation by $7$ .

$7 \frac{r D}{7} = 7 (f + m)$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$7 \frac{r D}{7} = 7 (f + m)$

Rewrite the expression.

$r D = 7 (f + m)$

Simplify the right side.

Apply the distributive property.

$r D = 7 f + 7 m$

Divide each term in $r D = 7 f + 7 m$ by $r$ and simplify.

Divide each term in $r D = 7 f + 7 m$ by $r$ .

$\frac{r D}{r} = \frac{7 f}{r} + \frac{7 m}{r}$

Simplify the left side.

Cancel the common factor of $r$ .

Cancel the common factor.

$\frac{r D}{r} = \frac{7 f}{r} + \frac{7 m}{r}$

Divide $D$ by $1$ .

$D = \frac{7 f}{r} + \frac{7 m}{r}$