Solve alpha=ax+b

$$\alpha = a x + b$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

$$ax+b=\alpha$$

Subtract b from both sides.

$$ax=\alpha -b$$

The equation is in standard form.

$$xa=\alpha -b$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{\alpha -b}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{\alpha -b}{x}$$

Solve for a

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

Steps for Solving Linear Equation

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

$$ax+b=\alpha$$

Subtract b from both sides.

$$ax=\alpha -b$$

The equation is in standard form.

$$xa=\alpha -b$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{\alpha -b}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{\alpha -b}{x}$$

Solve for b

$$b=\alpha -ax$$

Solution Steps

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

$$ax+b=\alpha$$

Subtract ax from both sides.

$$b=\alpha -ax$$