# How do you solve for b in A = 1/2h(B + b)?

Jul 23, 2015

You isolate it on one side of the equation.

#### Explanation:

To solve your expression for $b$, you need to isolate it on one side of the equation.

One way in which you can do that is by multiplying boths sides of the equation by 2 to get rid of the fraction.

$2 \cdot A = \cancel{2} \cdot \frac{1}{\cancel{2}} \cdot h \left(B + b\right)$

$2 A = h \left(B + b\right)$

Now divide both sides of the equation by $h$ to get

$\frac{2 A}{h} = \frac{\cancel{h}}{\cancel{h}} \cdot \left(B + b\right)$

$\frac{2 A}{h} = B + b$

Finally, move $B$ on the other side of the equation by subtracting it from both sides of the equation

$\frac{2 A}{h} - B = \cancel{B} - \cancel{B} + b$

And there you have it, $b$ is equal to

$b = \textcolor{g r e e n}{\frac{2 A}{h} - B}$