Question

How do you solve $\dfrac{2}{3}n+4=10-\dfrac{4}{3}n$ ?

Answer 1

Hint: We are given a equation as $\dfrac{2}{3}n+4=10-\dfrac{4}{3}n$ , we will learn that our equation has degree 1, then we will work on the definition of the solution, after that we will use various method like use of algebraic tool for hit and trial method, in the method of solving using algebraic tool we will use $\times ,\div ,+,-$ all these to simplify and solve.

Complete step by step answer:
We are given equation as $\dfrac{2}{3}n+4=10-\dfrac{4}{3}n$ , we can see that it just have 1 variable ‘n’ and that variable has highest degree as 1, so it mean we have a linear equation in one variable.
We are asked to solve means we have to look for that value of ‘n’ which will satisfy our given equation.
So, it means we look for that value which when inserted in place of ‘n’ then left side is the same as right.
Now we solve as follow –
As we have $\dfrac{2}{3}n+4=10-\dfrac{4}{3}n$.
Now we will subtract ‘4’ on both sides, so we have –
$\Rightarrow \dfrac{2}{3}n+4-4=10-\dfrac{4}{3}n-4$
By simplifying, we get –
$\Rightarrow \dfrac{2}{3}n=6-\dfrac{4}{3}n$
Now, we add $\dfrac{4}{3}n$ on both sides.
So, $\Rightarrow \dfrac{2}{3}n+\dfrac{4}{3}n=6-\dfrac{4}{3}n+\dfrac{4}{3}n$ .
By simplifying, we get –
$\Rightarrow \dfrac{2}{3}n+\dfrac{4}{3}n=6$
Now we add the left hand side term, we get –
$\Rightarrow \dfrac{6}{3}n=6$
Now to solve further, we will multiply both sides by ‘3’, so, we get –
$\Rightarrow \dfrac{6n}{3}\times 3=6\times 3$
By solving, we get –
 $\Rightarrow 6n=18$
Now, we divide both sides by ‘6’, we have –
$\Rightarrow \dfrac{6n}{6}=\dfrac{18}{6}$ .
So, we get –
$n=3$ as $\dfrac{18}{6}=3$ .
Hence, $n=3$ in the value which will satisfy our equation.

Note:
We can check our solution, we will put ‘n’ as ‘3’ in the left hand side and right hand side and see that they are the same or not.
Now left side is $\dfrac{2}{3}n+4$ .
Putting $n=3$ , we get –
$=\dfrac{2}{3}\times 3+4$ By simplifying, we get –
$\begin{align}
  & =2+4 \\
 & =6 \\
\end{align}$
Now the right side is $10-\dfrac{4}{3}n$ .
By putting $n=3$ , we get –
$\begin{align}
  & =10-\dfrac{4}{3}\times 3 \\
 & =10-4 \\
 & =6 \\
\end{align}$
Both sides are the same, so our solution is correct.
Another method to solve this is to use hit and trial, in such a method we guess the value of ‘n’, then put in the equation and see whether it satisfies the equation or not.
If the value which satisfies the equation, becomes the solution.