Solve 2θ/3θ=(2x)

$$\frac { 2 \theta } { 3 \theta } = ( 2 x )$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

$$\theta \neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3\theta .

$$2\theta =2x\times 3\theta$$

Multiply 2 and 3 to get 6.

$$2\theta =6x\theta$$

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

$$6x\theta =2\theta$$

The equation is in standard form.

$$6\theta x=2\theta$$

Divide both sides by 6\theta .

$$\frac{6\theta x}{6\theta }=\frac{2\theta }{6\theta }$$

Dividing by 6\theta undoes the multiplication by 6\theta .

$$x=\frac{2\theta }{6\theta }$$

Divide 2\theta by 6\theta .

$$x=\frac{1}{3}$$

Solve for θ

$$\theta \neq 0$$

$$x=\frac{1}{3}\text{ and }\theta \neq 0$$

Steps for Solving Linear Equation

Variable \theta cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3\theta .

$$2\theta =2x\times 3\theta$$

Multiply 2 and 3 to get 6.

$$2\theta =6x\theta$$

Subtract 6x\theta from both sides.

$$2\theta -6x\theta =0$$

Combine all terms containing \theta .

$$\left(2-6x\right)\theta =0$$

Divide 0 by 2-6x.

$$\theta =0$$

Variable \theta cannot be equal to 0.

$$\theta \in \emptyset$$