Solve S=1/2(a-b)xquad[b]

$$S = \frac { 1 } { 2 } ( a - b ) x \quad [ b ]$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{xb^{2}+2S}{bx}\text{, }&b\neq 0\text{ and }x\neq 0\\a\in \mathrm{C}\text{, }&\left(x=0\text{ or }b=0\right)\text{ and }S=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$S=\left(\frac{1}{2}a-\frac{1}{2}b\right)xb$$

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

$$S=\left(\frac{1}{2}ax-\frac{1}{2}bx\right)b$$

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

$$S=\frac{1}{2}axb-\frac{1}{2}xb^{2}$$

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

$$\frac{1}{2}axb-\frac{1}{2}xb^{2}=S$$

Add \frac{1}{2}xb^{2} to both sides.

$$\frac{1}{2}axb=S+\frac{1}{2}xb^{2}$$

The equation is in standard form.

$$\frac{bx}{2}a=\frac{xb^{2}}{2}+S$$

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

$$\frac{2\times \frac{bx}{2}a}{bx}=\frac{2\left(\frac{xb^{2}}{2}+S\right)}{bx}$$

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

$$a=\frac{2\left(\frac{xb^{2}}{2}+S\right)}{bx}$$

Divide S+\frac{xb^{2}}{2} by \frac{1}{2}xb.

$$a=b+\frac{2S}{bx}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{xb^{2}+2S}{bx}\text{, }&b\neq 0\text{ and }x\neq 0\\a\in \mathrm{R}\text{, }&\left(x=0\text{ or }b=0\right)\text{ and }S=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$S=\left(\frac{1}{2}a-\frac{1}{2}b\right)xb$$

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

$$S=\left(\frac{1}{2}ax-\frac{1}{2}bx\right)b$$

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

$$S=\frac{1}{2}axb-\frac{1}{2}xb^{2}$$

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

$$\frac{1}{2}axb-\frac{1}{2}xb^{2}=S$$

Add \frac{1}{2}xb^{2} to both sides.

$$\frac{1}{2}axb=S+\frac{1}{2}xb^{2}$$

The equation is in standard form.

$$\frac{bx}{2}a=\frac{xb^{2}}{2}+S$$

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

$$\frac{2\times \frac{bx}{2}a}{bx}=\frac{2\left(\frac{xb^{2}}{2}+S\right)}{bx}$$

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

$$a=\frac{2\left(\frac{xb^{2}}{2}+S\right)}{bx}$$

Divide S+\frac{xb^{2}}{2} by \frac{1}{2}xb.

$$a=b+\frac{2S}{bx}$$

Solve for S

$$S=\frac{bx\left(a-b\right)}{2}$$