Solve ax+2x=2a+4

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Subtract 2a from both sides.

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

Subtract 2x from both sides.

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

Combine all terms containing a.

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

Divide both sides by -2+x.

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

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

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

Divide 4-2x by -2+x.

$$a=-2$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(a+2\right)x=2a+4$$

Divide both sides by 2+a.

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

Dividing by 2+a undoes the multiplication by 2+a.

$$x=\frac{2a+4}{a+2}$$

Divide 4+2a by 2+a.

$$x=2$$

Solve for a

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

Steps for Solving Linear Equation

Subtract 2a from both sides.

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

Subtract 2x from both sides.

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

Combine all terms containing a.

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

Divide both sides by -2+x.

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

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

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

Divide 4-2x by -2+x.

$$a=-2$$

Solve for x

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

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(a+2\right)x=2a+4$$

Divide both sides by 2+a.

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

Dividing by 2+a undoes the multiplication by 2+a.

$$x=\frac{2a+4}{a+2}$$

Divide 4+2a by 2+a.

$$x=2$$