Solve the following linear equation.
$ \frac{n}{2}-\frac{3 n}{4}+\frac{5 n}{6}=21 $.

Given:

$\frac{n}{2}-\frac{3 n}{4}+\frac{5 n}{6}=21$.

To do:

We have to solve the given linear equation.

Solution: 

$\frac{n}{2}-\frac{3 n}{4}+\frac{5 n}{6}=21$

This implies,

$\frac{n(6) - 3n( 3) +5n(2)}{12}=21$

$\frac{6n - 9n + 10n}{12}  = 21$

$\frac{7n}{12}= 21$

$n =21 \times \frac{12}{7}$

$n =3 \times 12$

$n = 36$

The value of $n$ is $36$.