Solve 3x+(2x-4)y-7=0

$$3 x + ( 2 x - 4 ) y - 7 = 0$$

Solve for x

$$x=\frac{4y+7}{2y+3}$$

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

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-4 by y.

$$3x+2xy-4y-7=0$$

Add 4y to both sides. Anything plus zero gives itself.

$$3x+2xy-7=4y$$

Add 7 to both sides.

$$3x+2xy=4y+7$$

Combine all terms containing x.

$$\left(3+2y\right)x=4y+7$$

The equation is in standard form.

$$\left(2y+3\right)x=4y+7$$

Divide both sides by 2y+3.

$$\frac{\left(2y+3\right)x}{2y+3}=\frac{4y+7}{2y+3}$$

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

$$x=\frac{4y+7}{2y+3}$$

Solve for y

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

$$x\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-4 by y.

$$3x+2xy-4y-7=0$$

Subtract 3x from both sides. Anything subtracted from zero gives its negation.

$$2xy-4y-7=-3x$$

Add 7 to both sides.

$$2xy-4y=-3x+7$$

Combine all terms containing y.

$$\left(2x-4\right)y=-3x+7$$

The equation is in standard form.

$$\left(2x-4\right)y=7-3x$$

Divide both sides by -4+2x.

$$\frac{\left(2x-4\right)y}{2x-4}=\frac{7-3x}{2x-4}$$

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

$$y=\frac{7-3x}{2x-4}$$

Divide -3x+7 by -4+2x.

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