Question

How do you solve $2n+12=5n?$

Answer 1

Hint: In algebra, we add two numbers which consist of the same variable with the same exponent in a way that the variable remains the same while the coefficients get added to form the coefficient of the sum. Mathematically, $a{{x}^{n}}+b{{x}^{n}}=\left( a+b \right){{x}^{n}}$ where $a$ and $b$ are constants.

Complete step by step solution:
Let us consider the given algebraic equation in $n,$ $2n+12=5n.$
In this equation, we can see that there are two terms containing $n$ with the exponent $1.$
They are $2n$ and $5n.$
As we can see, the term $2n$ lies on the left-hand side and the term $5n$ lies on the right-hand side of the equation.
So, to solve the given equation, what we have to do is to transpose $5n$ from the right-hand side of the equation to the left-hand side while we transpose the constant term $12$ from the left-hand side to the right-hand side of the equation so that the similar terms lie on the same side. And then, we can add or subtract the terms accordingly.
The term $5n$ will become $-5n$ and the term $12$ will become $-12$ after we transpose these terms to the respective sides.
Now, let us transform these terms step by step as follows:
First, we are going to transpose $5n,$ we will get $2n-5n+12=0.$
Next, we are going to transpose $12,$ we will get $2n-5n=-12.$
Let us multiply the obtained equation with $-1,$ we will get $5n-2n=12.$
Now we subtract $2n$ from $5n,$ we will get $3n=12.$
To find the value of $n,$ we need to transpose $3$ from the left-hand side to the right-hand side.
We will get $n=\dfrac{12}{3}=4.$
Hence the solution of the given equation is $n=4.$

Note: In the above process, we can find the solution even if we don’t multiply the equation $2n-5n=-12$ with $-1.$ We will get $-3n=-12.$ From this, after we transpose $-3$ we will get $n=\dfrac{-12}{-3}=4.$