Question

Solve for n : \[\dfrac{n}{4} - 5 = \dfrac{n}{6} + \dfrac{1}{2}\]

Answer 1

Hint: This is just an equation or an expression with one variable. We have to solve it for n that is finding the value of n. we will shift the terms with n on one side and then we will start solving. It is required to find the LCM also.

Complete step by step solution:
Given that,
 \[\dfrac{n}{4} - 5 = \dfrac{n}{6} + \dfrac{1}{2}\]
Taking the n terms on one side we get,
 \[\dfrac{n}{4} - \dfrac{n}{6} = 5 + \dfrac{1}{2}\]
Taking the LCM on both sides,
 \[\dfrac{{6n - 4n}}{{4 \times 6}} = \dfrac{{5 \times 2 + 1}}{2}\]
On solving we get,
 \[\dfrac{{2n}}{{24}} = \dfrac{{11}}{2}\]
On cross multiplying we get,
 \[4n = 24 \times 11\]
Taking only n on one side,
 \[n = \dfrac{{24 \times 11}}{4}\]
On dividing by 4 w get,
 \[n = 6 \times 11\]
On multiplying we get,
 \[n = 66\]
This is the value of n.
So, the correct answer is “ \[n = 66\] ”.

Note: The expression given above is a single variable equation. So, it can be solved by one equation so given. But in general, to solve these types of problems the number of variables should be equal to the number of equations so given. Such two equations can be solved by cancellation method or substitution method etc.