Solve ax+x=b

$$a x + x = b$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{b}{x}-1\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$ax=b-x$$

The equation is in standard form.

$$xa=b-x$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide b-x by x.

$$a=\frac{b}{x}-1$$

Solve for a

$$\left\{\begin{matrix}a=\frac{b}{x}-1\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$ax=b-x$$

The equation is in standard form.

$$xa=b-x$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide b-x by x.

$$a=\frac{b}{x}-1$$

Solve for b

$$b=x\left(a+1\right)$$

Solution Steps

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

$$b=ax+x$$