Solve a_{n}=6n+5/14n

$$a _ { n } = \frac { 6 n + 5 } { 14 n }$$

Solve for n

$$n=\frac{5}{2\left(7a_{n}-3\right)}$$

$$a_{n}\neq \frac{3}{7}$$

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 14n.

$$a_{n}\times 14n=6n+5$$

Subtract 6n from both sides.

$$a_{n}\times 14n-6n=5$$

Combine all terms containing n.

$$\left(a_{n}\times 14-6\right)n=5$$

The equation is in standard form.

$$\left(14a_{n}-6\right)n=5$$

Divide both sides by 14a_{n}-6.

$$\frac{\left(14a_{n}-6\right)n}{14a_{n}-6}=\frac{5}{14a_{n}-6}$$

Dividing by 14a_{n}-6 undoes the multiplication by 14a_{n}-6.

$$n=\frac{5}{14a_{n}-6}$$

Divide 5 by 14a_{n}-6.

$$n=\frac{5}{2\left(7a_{n}-3\right)}$$

Variable n cannot be equal to 0.

$$n=\frac{5}{2\left(7a_{n}-3\right)}\text{, }n\neq 0$$

Solve for a_n

$$a_{n}=\frac{3}{7}+\frac{5}{14n}$$

$$n\neq 0$$