Solve 2x+ax=a-2

$$2 x + a x = a - 2$$

Solve for a

$$a=-\frac{2\left(x+1\right)}{x-1}$$

$$x\neq 1$$

Steps for Solving Linear Equation

Subtract a from both sides.

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

Subtract 2x from both sides.

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

Combine all terms containing a.

$$\left(x-1\right)a=-2-2x$$

The equation is in standard form.

$$\left(x-1\right)a=-2x-2$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)a}{x-1}=\frac{-2x-2}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$a=\frac{-2x-2}{x-1}$$

Divide -2-2x by x-1.

$$a=-\frac{2\left(x+1\right)}{x-1}$$

Solve for x

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

$$a\neq -2$$

Steps for Solving Linear Equation

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 2+a.

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

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

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