Solve 2y+5/y-7=x

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

Solve for x

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

$$y\neq 7$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y-7.

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

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

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

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

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

Combine all terms containing x.

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

Divide both sides by y-7.

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

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

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

Solve for y

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

$$x\neq 2$$

Steps for Solving Linear Equation

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

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

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

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

Subtract xy from both sides.

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

Subtract 5 from both sides.

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

Combine all terms containing y.

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

Divide both sides by 2-x.

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

Dividing by 2-x undoes the multiplication by 2-x.

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

Divide -7x-5 by 2-x.

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

Variable y cannot be equal to 7.

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