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# How do you solve $2n+1=4n-5$?

Last updated date: 16th Sep 2024
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Answer
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Hint: We separate the variables and the constants of the equation $2n+1=4n-5$. We apply the binary operation of addition for both variables and constants. The solutions of the variables and the constants will be added at the end to get the final answer. Then we equate them to 0 to find the answer for $n$.

Complete step-by-step solution:
The given equation $2n+1=4n-5$ is a linear equation of $n$. We need to simplify the equation by solving the variables and the constants separately.
All the terms in the equation of $2n+1=4n-5$ are either variable of $n$ or a constant. We first separate the variables.
\begin{align} & 2n+1=4n-5 \\ & \Rightarrow 2n+1-4n+5=0 \\ \end{align}
There are two such variables which are $2n$ and $4n$. The signs of the variables are both with coefficients being 2 and 4 respectively. The binary operation between them is subtraction which gives us $2n-4n=-2n$.
Now we take the constants. There are two such constants which are 1 and 5. The signs of the variables are both positive.
The binary operation between them is addition which gives us $1+5=6$.
The final equation becomes $-2n+6=0$.
Now we separate the variables and the constants to get $2n=6$.
Dividing both sides with 2 we get
\begin{align} & \dfrac{2n}{2}=\dfrac{6}{2} \\ & \Rightarrow n=3 \\ \end{align}
Therefore, the solution of the equation $2n+1=4n-5$ is $n=3$.

Note: We can verify the result of the equation $2n+1=4n-5$ by taking the value of n as $n=3$.
Therefore, the left-hand side of the equation becomes $2n+1=2\times 3+1=6+1=7$.
The right-hand side of the equation is $4n-5=4\times 3-5=12-5=7$.
Thus, verified for the equation $2n+1=4n-5$ the solution is $n=3$.