Question

Solve: \[3n + 7 = 25\]

Answer 1

Hint: Here we are asked to solve the given equation to find the unknown variable. This can be done by using the transposition method. In this method, the unknown variables are kept alone on one side of the equation by transferring the other terms to the other side of the equation. Then by simplifying that we will find the value of the unknown variable.

Complete step by step answer:
It is given that \[3n + 7 = 25\], we aim to solve this equation to find the value of the unknown variable. Here the unknown variable is \[n\]. So, we aim to find the value of the variable \[n\].
We are going to use the method called the transposition method to solve this equation. In the transposition method, the terms containing unknown variables are grouped on one side of the equation and other terms on the other side. Then by simplifying that we will find the value of the unknown variable.
Consider the given equation \[3n + 7 = 25\], here the unknown variable is \[n\] the term containing it is on the left-hand side along with another term. Now we will transpose that term to the other side of the equation.
\[ \Rightarrow 3n = 25 - 7\]
On simplifying the above equation, we get
\[ \Rightarrow 3n = 18\]
Now let us transpose the coefficient of the unknown variable to the other side.
\[ \Rightarrow n = \dfrac{{18}}{3}\]
On further simplification we get
\[ \Rightarrow n = 6\]
Thus, we have found the value of the unknown variable \[n\] as \[6\].

Note:
 In the above problem, we have used the transposition method to find the value of the unknown variable \[n\]. We can also use other methods like the trial-and-error method or the systematic method to solve that equation. But those methods are time-consuming when compared to the transposition method.