Solve the following linear equations:

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

 

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

Multiply both sides by the LCM of the denominators to get rid of fractional denominator.

Now transpose variables to one side and constants to another side to for linear equation.

n/2 - 3n/4 + 5n/6 = 21

LCM of the denominators is 12

Multiply the LCM on both sides

⇒ 12(n/2 - 3n/4 + 5n/6) = 12(21)

⇒ 6n - 9n + 10n = 252

⇒ 7n = 252

Hence, n = 252/7 = 36