Solve 6y+5/9y-7=x

$$\frac { 6 y + 5 } { 9 y - 7 } = x$$

Solve for x

$$x=-\frac{6y+5}{7-9y}$$

$$y\neq \frac{7}{9}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 9y-7.

$$6y+5=x\left(9y-7\right)$$

Use the distributive property to multiply x by 9y-7.

$$6y+5=9xy-7x$$

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

$$9xy-7x=6y+5$$

Combine all terms containing x.

$$\left(9y-7\right)x=6y+5$$

Divide both sides by 9y-7.

$$\frac{\left(9y-7\right)x}{9y-7}=\frac{6y+5}{9y-7}$$

Dividing by 9y-7 undoes the multiplication by 9y-7.

$$x=\frac{6y+5}{9y-7}$$

Solve for y

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

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

Steps for Solving Linear Equation

Variable y cannot be equal to \frac{7}{9} since division by zero is not defined. Multiply both sides of the equation by 9y-7.

$$6y+5=x\left(9y-7\right)$$

Use the distributive property to multiply x by 9y-7.

$$6y+5=9xy-7x$$

Subtract 9xy from both sides.

$$6y+5-9xy=-7x$$

Subtract 5 from both sides.

$$6y-9xy=-7x-5$$

Combine all terms containing y.

$$\left(6-9x\right)y=-7x-5$$

Divide both sides by 6-9x.

$$\frac{\left(6-9x\right)y}{6-9x}=\frac{-7x-5}{6-9x}$$

Dividing by 6-9x undoes the multiplication by 6-9x.

$$y=\frac{-7x-5}{6-9x}$$

Divide -7x-5 by 6-9x.

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

Variable y cannot be equal to \frac{7}{9}.

$$y=-\frac{7x+5}{3\left(2-3x\right)}\text{, }y\neq \frac{7}{9}$$