Solve 1/2-3y=x

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

Solve for x

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by -3y+2.

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

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

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

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

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 2-3y.

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

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

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

Solve for y

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Subtract 2x from both sides.

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

The equation is in standard form.

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

Divide both sides by -3x.

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

Dividing by -3x undoes the multiplication by -3x.

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

Divide 1-2x by -3x.

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

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

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