Question

How do you solve the equation $7-2n=n-14$ ?

Answer 1

Hint: First of all find the degree of this equation. As you can see that the degree of this equation is 1 because the highest power that the variable “n” has is 1 so the equation given is the linear equation in one variable which is “n”. Now, to solve this equation write the variable terms on the one side of the equation and constants on the other side and then use the basic algebra to solve them.

Complete step-by-step solution:
The equation given in the above problem is as follows:
$7-2n=n-14$………… Eq. (1)
In the above problem, we are asked to solve this equation this means there is some variable in this equation of which we have to find the value,
We know that the numbers are constants so the variable we can see in the above equation is “n”. Now, the degree of the variable “n” is 1. This means that this equation is a linear equation in one variable so to solve this equation, we are going to write all the variables on the one side of the equation and constants on the other side.
Adding 2n on both the sides of the equation (1) we get,
$7-2n+2n=n+2n-14$
From the L.H.S of the above equation, 2n will be cancelled out and we are left with:
$7=3n-14$
Adding 14 on both the sides we get,
$\begin{align}
  & 7+14=3n-14+14 \\
 & \Rightarrow 21=3n \\
\end{align}$
Dividing 3 on both the sides of the above equation we get,
$\begin{align}
  & \dfrac{21}{3}=n \\
 & \Rightarrow n=7 \\
\end{align}$
Hence, we have got the value of n as 7 in the above equation.

Note: We can check the value of “n” that we got above by substituting the value of “n” that we are getting in eq. (1) and then see whether that value of n is satisfying eq. (1) or not.
Substituting “n” as 7 in eq. (1) we get,
\[\begin{align}
  & 7-2n=n-14 \\
 & \Rightarrow 7-2\left( 7 \right)=7-14 \\
 & \Rightarrow 7-14=7-14 \\
 & \Rightarrow -7=-7 \\
\end{align}\]
As you can see that L.H.S = R.H.S so the value of “n” that we are getting above is correct.