Solve y=1/2x-5

$$y = \frac{ 1 }{ 2x-5 }$$

Solve for x

$$x=\frac{5}{2}+\frac{1}{2y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{5}{2} since division by zero is not defined. Multiply both sides of the equation by 2x-5.

$$y\left(2x-5\right)=1$$

Use the distributive property to multiply y by 2x-5.

$$2yx-5y=1$$

Add 5y to both sides.

$$2yx=1+5y$$

The equation is in standard form.

$$2yx=5y+1$$

Divide both sides by 2y.

$$\frac{2yx}{2y}=\frac{5y+1}{2y}$$

Dividing by 2y undoes the multiplication by 2y.

$$x=\frac{5y+1}{2y}$$

Divide 1+5y by 2y.

$$x=\frac{5}{2}+\frac{1}{2y}$$

Variable x cannot be equal to \frac{5}{2}.

$$x=\frac{5}{2}+\frac{1}{2y}\text{, }x\neq \frac{5}{2}$$

Solve for y

$$y=\frac{1}{2x-5}$$

$$x\neq \frac{5}{2}$$