Solve y=1/2x-2

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

Solve for x

$$x=1+\frac{1}{2y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-1\right).

$$y\times 2\left(x-1\right)=1$$

Use the distributive property to multiply y\times 2 by x-1.

$$2yx-y\times 2=1$$

Multiply -1 and 2 to get -2.

$$2yx-2y=1$$

Add 2y to both sides.

$$2yx=1+2y$$

The equation is in standard form.

$$2yx=2y+1$$

Divide both sides by 2y.

$$\frac{2yx}{2y}=\frac{2y+1}{2y}$$

Dividing by 2y undoes the multiplication by 2y.

$$x=\frac{2y+1}{2y}$$

Divide 1+2y by 2y.

$$x=1+\frac{1}{2y}$$

Variable x cannot be equal to 1.

$$x=1+\frac{1}{2y}\text{, }x\neq 1$$

Solve for y

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

$$x\neq 1$$