Solve x=9n-b/5n

$$x = \frac { 9 n - b } { 5 n }$$

Solve for b

$$b=n\left(9-5x\right)$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5n.

$$x\times 5n=9n-b$$

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

$$9n-b=x\times 5n$$

Subtract 9n from both sides.

$$-b=x\times 5n-9n$$

The equation is in standard form.

$$-b=5nx-9n$$

Divide both sides by -1.

$$\frac{-b}{-1}=\frac{n\left(5x-9\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$b=\frac{n\left(5x-9\right)}{-1}$$

Divide n\left(-9+5x\right) by -1.

$$b=9n-5nx$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{b}{5x-9}\text{, }&b\neq 0\text{ and }x\neq \frac{9}{5}\\n\neq 0\text{, }&b=0\text{ and }x=\frac{9}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5n.

$$x\times 5n=9n-b$$

Subtract 9n from both sides.

$$x\times 5n-9n=-b$$

Combine all terms containing n.

$$\left(x\times 5-9\right)n=-b$$

The equation is in standard form.

$$\left(5x-9\right)n=-b$$

Divide both sides by 5x-9.

$$\frac{\left(5x-9\right)n}{5x-9}=-\frac{b}{5x-9}$$

Dividing by 5x-9 undoes the multiplication by 5x-9.

$$n=-\frac{b}{5x-9}$$

Variable n cannot be equal to 0.

$$n=-\frac{b}{5x-9}\text{, }n\neq 0$$