Solve y=2x+2/5-x

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

Solve for x

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

$$y\neq -2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by -x+5.

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

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

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

Subtract 2x from both sides.

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

Subtract 5y from both sides.

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

Combine all terms containing x.

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

Divide both sides by -y-2.

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

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

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

Divide 2-5y by -y-2.

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

Variable x cannot be equal to 5.

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

Solve for y

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

$$x\neq 5$$