Solve 4(b-x)=2b+ax

$$4 ( b - x ) = 2 b + a x$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by b-x.

$$4b-4x=2b+ax$$

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

$$2b+ax=4b-4x$$

Subtract 2b from both sides.

$$ax=4b-4x-2b$$

Combine 4b and -2b to get 2b.

$$ax=2b-4x$$

The equation is in standard form.

$$xa=2b-4x$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{2b-4x}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{2b-4x}{x}$$

Divide 2b-4x by x.

$$a=\frac{2b}{x}-4$$

Solve for a

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

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by b-x.

$$4b-4x=2b+ax$$

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

$$2b+ax=4b-4x$$

Subtract 2b from both sides.

$$ax=4b-4x-2b$$

Combine 4b and -2b to get 2b.

$$ax=2b-4x$$

The equation is in standard form.

$$xa=2b-4x$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{2b-4x}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{2b-4x}{x}$$

Divide 2b-4x by x.

$$a=\frac{2b}{x}-4$$

Solve for b

$$b=\frac{x\left(a+4\right)}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by b-x.

$$4b-4x=2b+ax$$

Subtract 2b from both sides.

$$4b-4x-2b=ax$$

Combine 4b and -2b to get 2b.

$$2b-4x=ax$$

Add 4x to both sides.

$$2b=ax+4x$$

Divide both sides by 2.

$$\frac{2b}{2}=\frac{x\left(a+4\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$b=\frac{x\left(a+4\right)}{2}$$