Solve 2x/3/x=10/15

$$\frac{ \frac{ 2x }{ 3 } }{ x } = \frac{ 10 }{ 15 }$$

Solve for x

$$x\neq 0$$

Solution Steps

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15x, the least common multiple of x,15.

$$15\times \frac{2x}{3}=x\times 10$$

Cancel out 3, the greatest common factor in 15 and 3.

$$5\times 2x=x\times 10$$

Multiply 5 and 2 to get 10.

$$10x=x\times 10$$

Subtract x\times 10 from both sides.

$$10x-x\times 10=0$$

Combine 10x and -x\times 10 to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Variable x cannot be equal to 0.

$$x\in \mathrm{R}\setminus 0$$