Question

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

Answer 1

Solving Linear Equations in One Variable.

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

The LCM of $2$, $4$ and $6$ is $12$.

Therefore, convert the terms on the LHS into like fractions with $12$ as the denominator and simplify:

$\begin{array}{rcl}\frac{n\times 6}{2\times 6}-\frac{3n\times 3}{4\times 3}+\frac{5n\times 2}{6\times 2}& =& 21\\ & \Rightarrow & \frac{6n}{12}-\frac{9n}{12}+\frac{10n}{12}=21\\ & \Rightarrow & \frac{6n-9n+10n}{12}=21\\ & \Rightarrow & \frac{6n+n}{12}=21\\ & \Rightarrow & \frac{7n}{12}=21\\ & \Rightarrow & 7n=21\times 12\\ & \Rightarrow & n=\frac{21\times 12}{7}\\ & \Rightarrow & n=\frac{3\times 12}{1}\\ & \Rightarrow & n=36\end{array}$

Hence, the value of $n$ is $36$.