Solve y=3x+5/2x+2

$$y = \frac { 3 x + 5 } { 2 x + 2 }$$

Solve for x

$$x=-\frac{2y-5}{2y-3}$$

$$y\neq \frac{3}{2}$$

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).

$$y\times 2\left(x+1\right)=3x+5$$

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

$$2yx+y\times 2=3x+5$$

Subtract 3x from both sides.

$$2yx+y\times 2-3x=5$$

Subtract y\times 2 from both sides.

$$2yx-3x=5-y\times 2$$

Multiply -1 and 2 to get -2.

$$2yx-3x=5-2y$$

Combine all terms containing x.

$$\left(2y-3\right)x=5-2y$$

Divide both sides by 2y-3.

$$\frac{\left(2y-3\right)x}{2y-3}=\frac{5-2y}{2y-3}$$

Dividing by 2y-3 undoes the multiplication by 2y-3.

$$x=\frac{5-2y}{2y-3}$$

Variable x cannot be equal to -1.

$$x=\frac{5-2y}{2y-3}\text{, }x\neq -1$$

Solve for y

$$y=\frac{3x+5}{2\left(x+1\right)}$$

$$x\neq -1$$