Solve 3dx/dy+2=4

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

Solve for d

$$d\neq 0$$

$$y=\frac{3x}{2}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dy.

$$3dx+dy\times 2=4dy$$

Subtract 4dy from both sides.

$$3dx+dy\times 2-4dy=0$$

Combine dy\times 2 and -4dy to get -2dy.

$$3dx-2dy=0$$

Combine all terms containing d.

$$\left(3x-2y\right)d=0$$

Divide 0 by 3x-2y.

$$d=0$$

Variable d cannot be equal to 0.

$$d\in \emptyset$$

Solve for x

$$x=\frac{2y}{3}$$

$$d\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by dy.

$$3dx+dy\times 2=4dy$$

Subtract dy\times 2 from both sides.

$$3dx=4dy-dy\times 2$$

Combine 4dy and -dy\times 2 to get 2dy.

$$3dx=2dy$$

Divide both sides by 3d.

$$\frac{3dx}{3d}=\frac{2dy}{3d}$$

Dividing by 3d undoes the multiplication by 3d.

$$x=\frac{2dy}{3d}$$

Divide 2dy by 3d.

$$x=\frac{2y}{3}$$