Solve A=1/2hleft({b}_{1}+{b}_{2}right)

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

Solve for b_1

$$\left\{\begin{matrix}b_{1}=-b_{2}+\frac{2A}{h}\text{, }&h\neq 0\\b_{1}\in \mathrm{R}\text{, }&A=0\text{ and }h=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2}h by b_{1}+b_{2}.

$$A=\frac{1}{2}hb_{1}+\frac{1}{2}hb_{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2}hb_{1}+\frac{1}{2}hb_{2}=A$$

Subtract \frac{1}{2}hb_{2} from both sides.

$$\frac{1}{2}hb_{1}=A-\frac{1}{2}hb_{2}$$

The equation is in standard form.

$$\frac{h}{2}b_{1}=-\frac{b_{2}h}{2}+A$$

Divide both sides by \frac{1}{2}h.

$$\frac{2\times \frac{h}{2}b_{1}}{h}=\frac{2\left(-\frac{b_{2}h}{2}+A\right)}{h}$$

Dividing by \frac{1}{2}h undoes the multiplication by \frac{1}{2}h.

$$b_{1}=\frac{2\left(-\frac{b_{2}h}{2}+A\right)}{h}$$

Divide A-\frac{b_{2}h}{2} by \frac{1}{2}h.

$$b_{1}=-b_{2}+\frac{2A}{h}$$

Solve for A

$$A=\frac{h\left(b_{1}+b_{2}\right)}{2}$$