Solve (n-1)x=2(n+x)

$$( n - 1 ) x = 2 ( n + x )$$

Solve for n

$$n=\frac{3x}{x-2}$$

$$x\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-1 by x.

$$nx-x=2\left(n+x\right)$$

Use the distributive property to multiply 2 by n+x.

$$nx-x=2n+2x$$

Subtract 2n from both sides.

$$nx-x-2n=2x$$

Add x to both sides.

$$nx-2n=2x+x$$

Combine 2x and x to get 3x.

$$nx-2n=3x$$

Combine all terms containing n.

$$\left(x-2\right)n=3x$$

Divide both sides by x-2.

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

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

$$n=\frac{3x}{x-2}$$

Solve for x

$$x=\frac{2n}{n-3}$$

$$n\neq 3$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-1 by x.

$$nx-x=2\left(n+x\right)$$

Use the distributive property to multiply 2 by n+x.

$$nx-x=2n+2x$$

Subtract 2x from both sides.

$$nx-x-2x=2n$$

Combine -x and -2x to get -3x.

$$nx-3x=2n$$

Combine all terms containing x.

$$\left(n-3\right)x=2n$$

Divide both sides by n-3.

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

Dividing by n-3 undoes the multiplication by n-3.

$$x=\frac{2n}{n-3}$$