Q30. - Algebra 2

Question

Solve the equation and check the solution.

 

$\frac{n}{4}+\frac{n}{3}=\frac{1}{2}$

Step-by-Step Solution

Answer

The solution is $n=\frac{6}{7}$.

Step 1- Consider the equation.

Consider the equation $\frac{n}{4}+\frac{n}{3}=\frac{1}{2}$.

 

Multiply both sides of the equation by 12 and simplify.

Step 2- Step description.

$\begin{array}{l}\frac{n}{4}\left(12\right)+\frac{n}{3}\left(12\right)=\frac{1}{2}\left(12\right)\\ 3n+4n=6\\ 7n=6\end{array}$

Step 3- Step description.

Divide both sides of the equation by 7.

$\begin{array}{l}7n=6\\ n=\frac{6}{7}\end{array}$

Therefore, the solution is $n=\frac{6}{7}$.

Step 4- Verify the solution.

Substitute $n=\frac{6}{7}$ in the equation and simplify as follows:

 

$\begin{array}{c}\frac{n}{4}+\frac{n}{3}=\frac{1}{2}\\ \frac{\left(\raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$7$}\right.\right)}{4}+\frac{\left(\raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$7$}\right.\right)}{3}=\frac{1}{2}\\ \frac{6}{7\times 4}+\frac{6}{7\times 3}=\frac{1}{2}\\ \frac{3}{14}+\frac{2}{7}=\frac{1}{2}\\ \frac{3+4}{14}=\frac{1}{2}\\ \frac{7}{14}=\frac{1}{2}\\ \frac{1}{2}=\frac{1}{2}\end{array}$

 

Since the left-hand side of the equation is equal to the right-hand side of the equation, therefore, the solution is $n=\frac{6}{7}$.