Solve x_{n}=4/2n+1

$$x _ { n } = \frac { 4 } { 2 n + 1 }$$

Solve for n

$$n=-\frac{1}{2}+\frac{2}{x_{n}}$$

$$x_{n}\neq 0$$

Steps for Solving Linear Equation

Variable n cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2n+1.

$$x_{n}\left(2n+1\right)=4$$

Use the distributive property to multiply x_{n} by 2n+1.

$$2x_{n}n+x_{n}=4$$

Subtract x_{n} from both sides.

$$2x_{n}n=4-x_{n}$$

Divide both sides by 2x_{n}.

$$\frac{2x_{n}n}{2x_{n}}=\frac{4-x_{n}}{2x_{n}}$$

Dividing by 2x_{n} undoes the multiplication by 2x_{n}.

$$n=\frac{4-x_{n}}{2x_{n}}$$

Divide 4-x_{n} by 2x_{n}.

$$n=-\frac{1}{2}+\frac{2}{x_{n}}$$

Variable n cannot be equal to -\frac{1}{2}.

$$n=-\frac{1}{2}+\frac{2}{x_{n}}\text{, }n\neq -\frac{1}{2}$$

Solve for x_n

$$x_{n}=\frac{4}{2n+1}$$

$$n\neq -\frac{1}{2}$$