Solve n(x-2)+x=5(x-3)+9

$$n ( x - 2 ) + x = 5 ( x - 3 ) + 9$$

Solve for n

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

$$x\neq 2$$

Steps for Solving Linear Equation

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

$$nx-2n+x=5\left(x-3\right)+9$$

Use the distributive property to multiply 5 by x-3.

$$nx-2n+x=5x-15+9$$

Add -15 and 9 to get -6.

$$nx-2n+x=5x-6$$

Subtract x from both sides.

$$nx-2n=5x-6-x$$

Combine 5x and -x to get 4x.

$$nx-2n=4x-6$$

Combine all terms containing n.

$$\left(x-2\right)n=4x-6$$

Divide both sides by x-2.

$$\frac{\left(x-2\right)n}{x-2}=\frac{4x-6}{x-2}$$

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

$$n=\frac{4x-6}{x-2}$$

Divide 4x-6 by x-2.

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

Solve for x

$$x=-\frac{2\left(3-n\right)}{n-4}$$

$$n\neq 4$$

Steps for Solving Linear Equation

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

$$nx-2n+x=5\left(x-3\right)+9$$

Use the distributive property to multiply 5 by x-3.

$$nx-2n+x=5x-15+9$$

Add -15 and 9 to get -6.

$$nx-2n+x=5x-6$$

Subtract 5x from both sides.

$$nx-2n+x-5x=-6$$

Combine x and -5x to get -4x.

$$nx-2n-4x=-6$$

Add 2n to both sides.

$$nx-4x=-6+2n$$

Combine all terms containing x.

$$\left(n-4\right)x=-6+2n$$

The equation is in standard form.

$$\left(n-4\right)x=2n-6$$

Divide both sides by n-4.

$$\frac{\left(n-4\right)x}{n-4}=\frac{2n-6}{n-4}$$

Dividing by n-4 undoes the multiplication by n-4.

$$x=\frac{2n-6}{n-4}$$

Divide -6+2n by n-4.

$$x=\frac{2\left(n-3\right)}{n-4}$$