Question

How do you solve $4n - 12 = 12 - 4n$?

Answer 1

Hint: The given equation is a linear equation in terms of a single variable $n$. We will write the equation in a way that the terms with the variable $n$ are written on one side of the equality sign and the rest terms on another side of the equality sign. If the same number is added to both the sides or the same number is subtracted from both the sides, the equation remains undisturbed.

Complete step-by-step solution:
We have the equation as
$4n - 12 = 12 - 4n$
We first take the terms with the variable $n$ to the Left Hand Side or the LHS.
Since adding the same number to both the sides would not disturb the equation, we add $4n$ to both the LHS and the RHS. Thus, we get:
$
   \Rightarrow 4n - 12 + 4n = 12 - 4n + 4n \\
   \Rightarrow 8n - 12 = 12 - 0 \\
   \Rightarrow 8n - 12 = 12 \\
 $
Again, we add $12$ to both the LHS and the RHS. We get:
\[
   \Rightarrow 8n - 12 + 12 = 12 + 12 \\
   \Rightarrow 8n - 0 = 24 \\
   \Rightarrow 8n = 24 \\
 \]
Thus, we have:
$
  8n = 24 \\
   \Rightarrow n = \dfrac{{24}}{8} \\
   \Rightarrow n = 3 \\
 $
Hence, $x = 3$ is the solution to the given equation $4n - 12 = 12 - 4n$.

Note: In every equation, there is an equality sign between two expressions. The equality sign is like a weighing balance which separates the Left Hand Side (or the LHS) and the Right Hand Side (or the RHS). When the same number is subtracted from both the LHS and the RHS or the same number is added to both the LHS and the RHS, the equation remains unchanged. We can also check if the answer is correct or not by putting the value of $n$ in the equation given in the question. If LHS = RHS, the answer is said to be correct.