Solve 2x-2/4x+7=y

$$\frac{ 2x-2 }{ 4x+7 } =y$$

Solve for x

$$x=\frac{7y+2}{2\left(1-2y\right)}$$

$$y\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{7}{4} since division by zero is not defined. Multiply both sides of the equation by 4x+7.

$$2x-2=y\left(4x+7\right)$$

Use the distributive property to multiply y by 4x+7.

$$2x-2=4yx+7y$$

Subtract 4yx from both sides.

$$2x-2-4yx=7y$$

Add 2 to both sides.

$$2x-4yx=7y+2$$

Combine all terms containing x.

$$\left(2-4y\right)x=7y+2$$

Divide both sides by -4y+2.

$$\frac{\left(2-4y\right)x}{2-4y}=\frac{7y+2}{2-4y}$$

Dividing by -4y+2 undoes the multiplication by -4y+2.

$$x=\frac{7y+2}{2-4y}$$

Divide 7y+2 by -4y+2.

$$x=\frac{7y+2}{2\left(1-2y\right)}$$

Variable x cannot be equal to -\frac{7}{4}.

$$x=\frac{7y+2}{2\left(1-2y\right)}\text{, }x\neq -\frac{7}{4}$$

Solve for y

$$y=\frac{2\left(x-1\right)}{4x+7}$$

$$x\neq -\frac{7}{4}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4x+7.

$$2x-2=y\left(4x+7\right)$$

Use the distributive property to multiply y by 4x+7.

$$2x-2=4yx+7y$$

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

$$4yx+7y=2x-2$$

Combine all terms containing y.

$$\left(4x+7\right)y=2x-2$$

Divide both sides by 4x+7.

$$\frac{\left(4x+7\right)y}{4x+7}=\frac{2x-2}{4x+7}$$

Dividing by 4x+7 undoes the multiplication by 4x+7.

$$y=\frac{2x-2}{4x+7}$$

Divide -2+2x by 4x+7.

$$y=\frac{2\left(x-1\right)}{4x+7}$$