Question

How do you solve the equation \[2(n+2)=5n-5\]?

Answer 1

Hint: iven is the simple linear equation in one variable, we can solve it by rearranging the terms to get the value of the variable \[n\]. To simplify the equation, we have to use the distributive property of the algebra which states that,
\[a(b+c)=ab+ac\]
After this we can simply bring the variable terms to one side of the equation and constant to another side of the equation, to get a relation between them and by which we can get the solution value of the variable.

Complete step by step answer:
The given equation is: \[2(n+2)=5n-5\]
By using the distributive property, \[a(b+c)=ab+ac\]
We can simplify the bracket on the left-hand side to get,
\[\begin{align}
  & \Rightarrow 2n+2\times 2=5n-5 \\
 & \Rightarrow 2n+4=5n-5 \\
\end{align}\]
To solve this one variable linear equation, we have to put all the variable terms to one side of the equation and all other constants to the other side of the equation, to do this,
We subtract \[2n\] from both sides, and we get equation
\[4=3n-5\]
We add 5 to both sides of the equation
\[\begin{align}
  & \Rightarrow 4+5=3n-5+5 \\
 & \Rightarrow 3n=9 \\
\end{align}\]
We divide both sides of the equation by 3
\[\begin{align}
  & \Rightarrow \dfrac{3n}{3}=\dfrac{9}{3} \\
 & \therefore n=3 \\
\end{align}\]

Hence, the solution of the given equation is, \[n=3\] .

Note: For these types of questions, you should try to make the necessary calculations and find the value of the variable. These types of questions are not very difficult, but you need to be careful about calculations as well as sign convention of the variables and constants after simplifying the equation.
These types of problems can also be solved by the hit and error method, but this method will not be always easy so we should not use this much.