Solve A=1/2(b)(xy-4)

$$A = \frac { 1 } { 2 } ( b ) ( x y - 4 )$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{2A}{4-xy}\text{, }&y=0\text{ or }x\neq \frac{4}{y}\\b\in \mathrm{C}\text{, }&A=0\text{ and }x=\frac{4}{y}\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2}b by xy-4.

$$A=\frac{1}{2}bxy-2b$$

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

$$\frac{1}{2}bxy-2b=A$$

Combine all terms containing b.

$$\left(\frac{1}{2}xy-2\right)b=A$$

The equation is in standard form.

$$\left(\frac{xy}{2}-2\right)b=A$$

Divide both sides by \frac{1}{2}xy-2.

$$\frac{\left(\frac{xy}{2}-2\right)b}{\frac{xy}{2}-2}=\frac{A}{\frac{xy}{2}-2}$$

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

$$b=\frac{A}{\frac{xy}{2}-2}$$

Divide A by \frac{1}{2}xy-2.

$$b=\frac{2A}{xy-4}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{2A}{4-xy}\text{, }&y=0\text{ or }x\neq \frac{4}{y}\\b\in \mathrm{R}\text{, }&A=0\text{ and }x=\frac{4}{y}\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2}b by xy-4.

$$A=\frac{1}{2}bxy-2b$$

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

$$\frac{1}{2}bxy-2b=A$$

Combine all terms containing b.

$$\left(\frac{1}{2}xy-2\right)b=A$$

The equation is in standard form.

$$\left(\frac{xy}{2}-2\right)b=A$$

Divide both sides by \frac{1}{2}xy-2.

$$\frac{\left(\frac{xy}{2}-2\right)b}{\frac{xy}{2}-2}=\frac{A}{\frac{xy}{2}-2}$$

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

$$b=\frac{A}{\frac{xy}{2}-2}$$

Divide A by \frac{1}{2}xy-2.

$$b=\frac{2A}{xy-4}$$

Solve for A

$$A=\frac{b\left(xy-4\right)}{2}$$