Solve 8(b-x)=4b+ax

$$8 ( b - x ) = 4 b + a x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{4b}{x}-8\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 8 by b-x.

$$8b-8x=4b+ax$$

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

$$4b+ax=8b-8x$$

Subtract 4b from both sides.

$$ax=8b-8x-4b$$

Combine 8b and -4b to get 4b.

$$ax=4b-8x$$

The equation is in standard form.

$$xa=4b-8x$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{4b-8x}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{4b-8x}{x}$$

Divide 4b-8x by x.

$$a=\frac{4b}{x}-8$$

Solve for a

$$\left\{\begin{matrix}a=\frac{4b}{x}-8\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 8 by b-x.

$$8b-8x=4b+ax$$

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

$$4b+ax=8b-8x$$

Subtract 4b from both sides.

$$ax=8b-8x-4b$$

Combine 8b and -4b to get 4b.

$$ax=4b-8x$$

The equation is in standard form.

$$xa=4b-8x$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{4b-8x}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{4b-8x}{x}$$

Divide 4b-8x by x.

$$a=\frac{4b}{x}-8$$

Solve for b

$$b=\frac{x\left(a+8\right)}{4}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 8 by b-x.

$$8b-8x=4b+ax$$

Subtract 4b from both sides.

$$8b-8x-4b=ax$$

Combine 8b and -4b to get 4b.

$$4b-8x=ax$$

Add 8x to both sides.

$$4b=ax+8x$$

Divide both sides by 4.

$$\frac{4b}{4}=\frac{x\left(a+8\right)}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$b=\frac{x\left(a+8\right)}{4}$$