Question

How do you solve \[n-3n=14-4n\]?

Answer 1

Hint: Rearrange the terms of the given equation by taking the terms containing the variable ‘n’ to the L.H.S. and take the constant terms to the R.H.S. Now, apply the simple arithmetic operations: - addition, subtraction, multiplication and division, whichever needed, to simplify the equation. Find the value of ‘n’ to get the answer.

Complete step by step answer:
We have been provided with the equation: - \[n-3n=14-4n\] and we are asked to solve this equation. That means we have to find the value of n.
As we can see that the given equation is a linear equation in one variable which is ‘n’, so now taking the terms containing the variable ‘n’ to the left-hand side (L.H.S.) and the constant terms to the right-hand side (R.H.S.), we get,
\[\begin{align}
  & \Rightarrow n-3n+4n=14 \\
 & \Rightarrow 5n-3n=14 \\
 & \Rightarrow 2n=14 \\
\end{align}\]
Dividing both the sides with 2 and cancelling the common factors on both the sides, we get,
\[\Rightarrow \dfrac{2n}{2}=\dfrac{14}{2}\]
\[\Rightarrow n=7\]
Hence, the value of n is 7.

Note:
One may note that we have been provided with a single equation only. The reason is that we have to find the value of only one variable, that is ‘n’. So, in general if we have to solve an equation having ‘m’ number of variables then we should be provided with ‘m’ number of equations. Now, one can check the answer by substituting the obtained value of ‘n’ in the equation provided in the question. We have to determine the value of L.H.S. and R.H.S. separately and if they are equal then our answer is correct.