Solve x-1/3x+2=y

$$\frac{ x-1 }{ 3x+2 } =y$$

Solve for x

$$x=\frac{2y+1}{1-3y}$$

$$y\neq \frac{1}{3}$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{2}{3} since division by zero is not defined. Multiply both sides of the equation by 3x+2.

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

Use the distributive property to multiply y by 3x+2.

$$x-1=3yx+2y$$

Subtract 3yx from both sides.

$$x-1-3yx=2y$$

Add 1 to both sides.

$$x-3yx=2y+1$$

Combine all terms containing x.

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

Divide both sides by -3y+1.

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

Dividing by -3y+1 undoes the multiplication by -3y+1.

$$x=\frac{2y+1}{1-3y}$$

Variable x cannot be equal to -\frac{2}{3}.

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

Solve for y

$$y=\frac{x-1}{3x+2}$$

$$x\neq -\frac{2}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3x+2.

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

Use the distributive property to multiply y by 3x+2.

$$x-1=3yx+2y$$

Swap sides so that all variable terms are on the left hand side.

$$3yx+2y=x-1$$

Combine all terms containing y.

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

Divide both sides by 3x+2.

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

Dividing by 3x+2 undoes the multiplication by 3x+2.

$$y=\frac{x-1}{3x+2}$$