Solve y^-1(x)=3x+2

$${ y }^{ -1 } (x)=3x+2$$

Solve for x

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

$$y\neq \frac{1}{3}\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Subtract 3x from both sides.

$$y^{-1}x-3x=2$$

Reorder the terms.

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

Multiply both sides of the equation by y.

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

Reorder the terms.

$$-3xy+x=2y$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -3y+1.

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

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

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

Solve for y

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

$$x\neq 0\text{ and }x\neq -\frac{2}{3}$$

Steps for Solving Linear Equation

Reorder the terms.

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

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$1x=3xy+y\times 2$$

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

$$3xy+y\times 2=1x$$

Reorder the terms.

$$3xy+2y=x$$

Combine all terms containing y.

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

Divide both sides by 3x+2.

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

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

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

Variable y cannot be equal to 0.

$$y=\frac{x}{3x+2}\text{, }y\neq 0$$