Question

How do you solve: \[1-\left( 2n+9 \right)=4\left( n-2 \right)\]?

Answer 1

Hint: Simplify the terms in R.H.S by multiplying the constant 4 with each term inside the bracket. Rearrange the terms of the equation by taking the terms containing the variable ‘n’ to the L.H.S. and taking the constant terms to the R.H.S. Now, apply the simple arithmetic operations like: - addition, subtraction, multiplication and division, whichever needed, to simplify the equation. Find the value of ‘n’ to get the answer.

Complete step by step solution:
We have been provided with the equation: \[1-\left( 2n+9 \right)=4\left( n-2 \right)\] and we are asked to solve this equation. That means we have to find the value of n.
Simplifying the equation by removing the bracket we get,
\[\begin{align}
  & \Rightarrow 1-\left( 2n+9 \right)=4n-8 \\
 & \Rightarrow 1-2n-9=4n-8 \\
\end{align}\]
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,
\[\begin{align}
  & \Rightarrow -2n-4n=-1+9-8 \\
 & \Rightarrow -6n=9-9 \\
 & \Rightarrow -6n=0 \\
\end{align}\]
Dividing both the sides with -6 and using the fact that ‘0 divided by any non – zero number equals 0’, we get,
\[\Rightarrow \dfrac{-6n}{-6}=\dfrac{0}{-6}\]
On simplifying we get,
\[\Rightarrow n=0\]

Hence, the value of n is 0.

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. Substitute n = 0 in the provided equation and if we get L.H.S = R.H.S, it means our answer is correct.