Solve S=1/3(x+b)a

$$S = \frac { 1 } { 3 } ( x + b ) a$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{3S}{x+b}\text{, }&x\neq -b\\a\in \mathrm{C}\text{, }&S=0\text{ and }x=-b\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by x+b.

$$S=\left(\frac{1}{3}x+\frac{1}{3}b\right)a$$

Use the distributive property to multiply \frac{1}{3}x+\frac{1}{3}b by a.

$$S=\frac{1}{3}xa+\frac{1}{3}ba$$

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

$$\frac{1}{3}xa+\frac{1}{3}ba=S$$

Combine all terms containing a.

$$\left(\frac{1}{3}x+\frac{1}{3}b\right)a=S$$

The equation is in standard form.

$$\frac{x+b}{3}a=S$$

Divide both sides by \frac{1}{3}x+\frac{1}{3}b.

$$\frac{3\times \frac{x+b}{3}a}{x+b}=\frac{3S}{x+b}$$

Dividing by \frac{1}{3}x+\frac{1}{3}b undoes the multiplication by \frac{1}{3}x+\frac{1}{3}b.

$$a=\frac{3S}{x+b}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{3S}{x+b}\text{, }&x\neq -b\\a\in \mathrm{R}\text{, }&S=0\text{ and }x=-b\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by x+b.

$$S=\left(\frac{1}{3}x+\frac{1}{3}b\right)a$$

Use the distributive property to multiply \frac{1}{3}x+\frac{1}{3}b by a.

$$S=\frac{1}{3}xa+\frac{1}{3}ba$$

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

$$\frac{1}{3}xa+\frac{1}{3}ba=S$$

Combine all terms containing a.

$$\left(\frac{1}{3}x+\frac{1}{3}b\right)a=S$$

The equation is in standard form.

$$\frac{x+b}{3}a=S$$

Divide both sides by \frac{1}{3}x+\frac{1}{3}b.

$$\frac{3\times \frac{x+b}{3}a}{x+b}=\frac{3S}{x+b}$$

Dividing by \frac{1}{3}x+\frac{1}{3}b undoes the multiplication by \frac{1}{3}x+\frac{1}{3}b.

$$a=\frac{3S}{x+b}$$

Solve for S

$$S=\frac{a\left(x+b\right)}{3}$$