Solve for b h=m+1/5rb

$h = m + \frac{1}{5} r b$

Step 1

Rewrite the equation as $m + \frac{1}{5} \cdot (r b) = h$ .

$m + \frac{1}{5} \cdot (r b) = h$

Step 2

Multiply $\frac{1}{5} (r b)$ .

Combine $r$ and $\frac{1}{5}$ .

$m + \frac{r}{5} b = h$

Combine $\frac{r}{5}$ and $b$ .

$m + \frac{r b}{5} = h$

Step 3

Subtract $m$ from both sides of the equation.

$\frac{r b}{5} = h - m$

Step 4

Multiply both sides of the equation by $5$ .

$5 \frac{r b}{5} = 5 (h - m)$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{r b}{5} = 5 (h - m)$

Rewrite the expression.

$r b = 5 (h - m)$

Simplify the right side.

Simplify $5 (h - m)$ .

Apply the distributive property.

$r b = 5 h + 5 (- m)$

Multiply $- 1$ by $5$ .

$r b = 5 h - 5 m$

Step 6

Divide each term in $r b = 5 h - 5 m$ by $r$ and simplify.

Divide each term in $r b = 5 h - 5 m$ by $r$ .

$\frac{r b}{r} = \frac{5 h}{r} + \frac{- 5 m}{r}$

Simplify the left side.

Cancel the common factor of $r$ .

Cancel the common factor.

$\frac{r b}{r} = \frac{5 h}{r} + \frac{- 5 m}{r}$

Divide $b$ by $1$ .

$b = \frac{5 h}{r} + \frac{- 5 m}{r}$

Simplify the right side.

Move the negative in front of the fraction.

$b = \frac{5 h}{r} - \frac{5 m}{r}$