Solve ax+8=4x+2a

$$a x + 8 = 4 x + 2 a$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=4\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2a from both sides.

$$ax+8-2a=4x$$

Subtract 8 from both sides.

$$ax-2a=4x-8$$

Combine all terms containing a.

$$\left(x-2\right)a=4x-8$$

Divide both sides by -2+x.

$$\frac{\left(x-2\right)a}{x-2}=\frac{4x-8}{x-2}$$

Dividing by -2+x undoes the multiplication by -2+x.

$$a=\frac{4x-8}{x-2}$$

Divide -8+4x by -2+x.

$$a=4$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=2\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&a=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4x from both sides.

$$ax+8-4x=2a$$

Subtract 8 from both sides.

$$ax-4x=2a-8$$

Combine all terms containing x.

$$\left(a-4\right)x=2a-8$$

Divide both sides by -4+a.

$$\frac{\left(a-4\right)x}{a-4}=\frac{2a-8}{a-4}$$

Dividing by -4+a undoes the multiplication by -4+a.

$$x=\frac{2a-8}{a-4}$$

Divide -8+2a by -4+a.

$$x=2$$

Solve for a

$$\left\{\begin{matrix}\\a=4\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2a from both sides.

$$ax+8-2a=4x$$

Subtract 8 from both sides.

$$ax-2a=4x-8$$

Combine all terms containing a.

$$\left(x-2\right)a=4x-8$$

Divide both sides by -2+x.

$$\frac{\left(x-2\right)a}{x-2}=\frac{4x-8}{x-2}$$

Dividing by -2+x undoes the multiplication by -2+x.

$$a=\frac{4x-8}{x-2}$$

Divide -8+4x by -2+x.

$$a=4$$

Solve for x

$$\left\{\begin{matrix}\\x=2\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&a=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4x from both sides.

$$ax+8-4x=2a$$

Subtract 8 from both sides.

$$ax-4x=2a-8$$

Combine all terms containing x.

$$\left(a-4\right)x=2a-8$$

Divide both sides by -4+a.

$$\frac{\left(a-4\right)x}{a-4}=\frac{2a-8}{a-4}$$

Dividing by -4+a undoes the multiplication by -4+a.

$$x=\frac{2a-8}{a-4}$$

Divide -8+2a by -4+a.

$$x=2$$