Question

How do you solve $2n+14=6n-22$ ?

Answer 1

Hint: We are given a one-degree polynomial equation in n-variable which has one term of n-variable and one constant term each on the left-hand side and the right-hand side. We shall first transpose all the constant terms to the right hand side and the n-variable terms to the left hand side and perform simple addition or subtraction according to the equation. Then, we will make the coefficient of x equal to 1 to obtain our final solution of the given equation.

Complete step by step solution:
Given that $2n+14=6n-22$.
The constant term on the left hand side is 14 and the constant term on the right hand side is -22. We shall transpose 14 to the right hand side and subtract it from -22. Also, we shall transpose the term 6n to the left hand side.
$\Rightarrow 2n-6n=-22-14$
$\Rightarrow -4n=-36$
We will now cancel the negative sign from both sides.
$\Rightarrow 4n=36$
In order to make the coefficient of x equal to 1, we will now divide the entire equation by 4.
$\Rightarrow \dfrac{4n}{4}=\dfrac{36}{4}$
$\Rightarrow n=9$
The solution of the equation is the value of the variable-n which will be obtained on solving the equation and we have calculated variable x equal to 9.
Therefore, the solution of the given equation $2n+14=6n-22$ is $n=9$.

Note: One possible mistake could be made while transposing terms from the left hand side of the equation to the right hand side and vice versa. Sometimes, we tend to forget about reversing the sign of the term which is being transposed but this could make our final solution completely incorrect. Thus, we must pay special attention to it.