# H=2A/B+b for B?

Mar 5, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{b}$ from each side of the equation to isolate the $B$ term while keeping the equation balanced:

$H - \textcolor{red}{b} = \frac{2 A}{B} + b - \textcolor{red}{b}$

$H - b = \frac{2 A}{B} + 0$

$H - b = \frac{2 A}{B}$

Now, multiply each side of the equation by $\frac{\textcolor{red}{B}}{\textcolor{b l u e}{H - b}}$ to solve for $B$:

$\frac{\textcolor{red}{B}}{\textcolor{b l u e}{H - b}} \times \left(H - b\right) = \frac{\textcolor{red}{B}}{\textcolor{b l u e}{H - b}} \times \frac{2 A}{B}$

$\frac{\textcolor{red}{B}}{\cancel{\textcolor{b l u e}{H - b}}} \times \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{\left(H - b\right)}}} = \frac{\cancel{\textcolor{red}{B}}}{\textcolor{b l u e}{H - b}} \times \frac{2 A}{\textcolor{red}{\cancel{\textcolor{b l a c k}{B}}}}$

$B = \frac{2 A}{H - b}$