Solve (lambda-2)x=lambda

$$( \lambda - 2 ) x = \lambda$$

Solve for x

$$x=\frac{\lambda }{\lambda -2}$$

$$\lambda \neq 2$$

Steps for Solving Linear Equation

Divide both sides by \lambda -2.

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

Dividing by \lambda -2 undoes the multiplication by \lambda -2.

$$x=\frac{\lambda }{\lambda -2}$$

Solve for λ

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

$$x\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply \lambda -2 by x.

$$\lambda x-2x=\lambda$$

Subtract \lambda from both sides.

$$\lambda x-2x-\lambda =0$$

Add 2x to both sides. Anything plus zero gives itself.

$$\lambda x-\lambda =2x$$

Combine all terms containing \lambda .

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

Divide both sides by x-1.

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

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

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