Question

How do you solve \[8n - 12 = - 12n + 8\]?

Answer 1

Hint: In the given problem we need to solve this for ‘n’. We can solve this using the transposition method. The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolating the variable (or the unknown quantity). That is we group the ‘n’ terms one side and constants on the other side of the equation.

Complete step-by-step solution:
Given, \[8n - 12 = - 12n + 8\].
We transpose ‘\[ - 12n\]’ which is present in the right hand side of the equation to the left hand side of the equation by adding ‘12n’ on the left hand side of the equation. Then
\[\Rightarrow 8n + 12n - 12 = 8\]
\[\Rightarrow 20n - 12 = 8\]
We transpose negative 12 to the right hand side of the equation by adding 12 on the right hand side of the equation. Then
\[\Rightarrow 20n = 8 + 12\].
\[\Rightarrow 20n = 20\]
Divide the whole equation by 20, we have:
\[\Rightarrow n = \dfrac{{20}}{{20}}\]
Cancelling we have:
\[ \Rightarrow n = 1\]. This is the required answer.

Note: We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘n’ in the given problem.
\[8(1) - 12 = - 12(1) + 8\]
\[8 - 12 = - 12 + 8\]
\[ \Rightarrow - 4 = - 4\]
Hence the obtained answer is correct.
If we want to transpose a positive number to the other side of the equation we subtract the same number on that side (vice versa). Similarly if we have multiplication we use division to transpose. If we have division we use multiplication to transpose. Follow the same procedure for these kinds of problems.