Solve x=5+7y/3y-2

$$x = \frac { 5 + 7 y } { 3 y - 2 }$$

Solve for y

$$y=\frac{2x+5}{3x-7}$$

$$x\neq \frac{7}{3}$$

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.

$$x\left(3y-2\right)=5+7y$$

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

$$3xy-2x=5+7y$$

Subtract 7y from both sides.

$$3xy-2x-7y=5$$

Add 2x to both sides.

$$3xy-7y=5+2x$$

Combine all terms containing y.

$$\left(3x-7\right)y=5+2x$$

The equation is in standard form.

$$\left(3x-7\right)y=2x+5$$

Divide both sides by 3x-7.

$$\frac{\left(3x-7\right)y}{3x-7}=\frac{2x+5}{3x-7}$$

Dividing by 3x-7 undoes the multiplication by 3x-7.

$$y=\frac{2x+5}{3x-7}$$

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

$$y=\frac{2x+5}{3x-7}\text{, }y\neq \frac{2}{3}$$

Solve for x

$$x=\frac{7y+5}{3y-2}$$

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