Solve 2v/x+10=200/x

$$\frac { 2 v } { x + 10 } = \frac { 200 } { x }$$

Solve for v

$$v=100+\frac{1000}{x}$$

$$x\neq -10\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(x+10\right), the least common multiple of x+10,x.

$$x\times 2v=\left(x+10\right)\times 200$$

Use the distributive property to multiply x+10 by 200.

$$x\times 2v=200x+2000$$

The equation is in standard form.

$$2xv=200x+2000$$

Divide both sides by 2x.

$$\frac{2xv}{2x}=\frac{200x+2000}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$v=\frac{200x+2000}{2x}$$

Divide 2000+200x by 2x.

$$v=100+\frac{1000}{x}$$

Solve for x

$$x=\frac{1000}{v-100}$$

$$v\neq 0\text{ and }v\neq 100$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -10,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+10\right), the least common multiple of x+10,x.

$$x\times 2v=\left(x+10\right)\times 200$$

Use the distributive property to multiply x+10 by 200.

$$x\times 2v=200x+2000$$

Subtract 200x from both sides.

$$x\times 2v-200x=2000$$

Combine all terms containing x.

$$\left(2v-200\right)x=2000$$

Divide both sides by 2v-200.

$$\frac{\left(2v-200\right)x}{2v-200}=\frac{2000}{2v-200}$$

Dividing by 2v-200 undoes the multiplication by 2v-200.

$$x=\frac{2000}{2v-200}$$

Divide 2000 by 2v-200.

$$x=\frac{1000}{v-100}$$

Variable x cannot be equal to any of the values -10,0.

$$x=\frac{1000}{v-100}\text{, }x\neq -10\text{ and }x\neq 0$$