Solve for B A=1/2h(B+b) ; for B

$A = \frac{1}{2} h (B + b)$ ; for $B$

Rewrite the equation as $\frac{1}{2} \cdot (h (B + b)) = A$ .

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

Multiply both sides of the equation by $2$ .

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

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot (h (B + b)))$ .

Apply the distributive property.

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

Apply the distributive property.

$2 (\frac{1}{2} (h B) + \frac{1}{2} (h b)) = 2 A$

Multiply $\frac{1}{2} (h B)$ .

Combine $h$ and $\frac{1}{2}$ .

$2 (\frac{h}{2} B + \frac{1}{2} (h b)) = 2 A$

Combine $\frac{h}{2}$ and $B$ .

$2 (\frac{h B}{2} + \frac{1}{2} (h b)) = 2 A$

$2 (\frac{h B}{2} + \frac{1}{2} (h b)) = 2 A$

Multiply $\frac{1}{2} (h b)$ .

Combine $h$ and $\frac{1}{2}$ .

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

Combine $\frac{h}{2}$ and $b$ .

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

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$h B + h b = 2 A$

$h B + h b = 2 A$

$h B + h b = 2 A$

$h B + h b = 2 A$

Subtract $h b$ from both sides of the equation.

$h B = 2 A - h b$

Divide each term in $h B = 2 A - h b$ by $h$ and simplify.

Divide each term in $h B = 2 A - h b$ by $h$ .

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

Simplify the left side.

Cancel the common factor of $h$ .

Cancel the common factor.

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

Divide $B$ by $1$ .

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

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

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $h$ .

Cancel the common factor.

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

Divide $- 1 b$ by $1$ .

$B = \frac{2 A}{h} - 1 b$

$B = \frac{2 A}{h} - 1 b$

Rewrite $- 1 b$ as $- b$ .

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

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

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

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

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