Solve y=x-5/2-x

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

Solve for x

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

$$y\neq -1$$

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 -x+2.

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

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

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

Subtract x from both sides.

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

Subtract 2y from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -y-1.

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

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

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

Divide -5-2y by -y-1.

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

Variable x cannot be equal to 2.

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

Solve for y

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

$$x\neq 2$$