Solve y=x-5/2x-4

$$y = \frac { x - 5 } { 2 x - 4 }$$

Solve for x

$$x=-\frac{5-4y}{2y-1}$$

$$y\neq \frac{1}{2}$$

Steps for Solving Linear Equation

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

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

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

$$2yx-2y\times 2=x-5$$

Multiply -2 and 2 to get -4.

$$2yx-4y=x-5$$

Subtract x from both sides.

$$2yx-4y-x=-5$$

Add 4y to both sides.

$$2yx-x=-5+4y$$

Combine all terms containing x.

$$\left(2y-1\right)x=-5+4y$$

The equation is in standard form.

$$\left(2y-1\right)x=4y-5$$

Divide both sides by 2y-1.

$$\frac{\left(2y-1\right)x}{2y-1}=\frac{4y-5}{2y-1}$$

Dividing by 2y-1 undoes the multiplication by 2y-1.

$$x=\frac{4y-5}{2y-1}$$

Variable x cannot be equal to 2.

$$x=\frac{4y-5}{2y-1}\text{, }x\neq 2$$

Solve for y

$$y=-\frac{5-x}{2\left(x-2\right)}$$

$$x\neq 2$$