Question

Solve the following Equation $2y+\dfrac{5}{2}=\dfrac{37}{2}$.

Answer 1

Hint: In this problem we will reduce the given equation in step by step manner. We will use some arithmetic operation to get the value of $y$. Based on the given equation we will use the different arithmetic operations. We need to keep the variable on one side of the equation. Here there is an addition of $\dfrac{5}{2}$ to the equation, so we will use the subtract operation and subtract the same value that is along with the variable. Then we will get the value of $2y$. Now by dividing the equation with $2$ we will get the value of $y$.

Complete step-by-step answer:
Given that, $2y+\dfrac{5}{2}=\dfrac{37}{2}$
Subtracting the term which is along the variable $y$ in the above equation, then we will get
$2y+\dfrac{5}{2}-\dfrac{5}{2}=\dfrac{37}{2}-\dfrac{5}{2}$
We know that $a-a=0$, then
$2y=\dfrac{37}{2}-\dfrac{5}{2}$
Now taking $2$ as common in the denominator, then we will get
$\begin{align}
  & 2y=\dfrac{1}{2}\left( 37-5 \right) \\
 & \Rightarrow 2y=\dfrac{1}{2}\left( 32 \right) \\
 & \Rightarrow 2y=16 \\
\end{align}$
Now we have the value of $2y$, to calculate the value of $y$ we are going to divide the above equation with $2$, then we will have
$\begin{align}
  & \dfrac{2y}{2}=\dfrac{16}{2} \\
 & \therefore y=8 \\
\end{align}$

Note: We can also solve the above problem in different methods. We can take LCM on the LHS side and equate them to get the result.
Given $2y+\dfrac{5}{2}=\dfrac{37}{2}$
Taking LCM on LHS, then we will get
$\begin{align}
  & \dfrac{2\left( 2y \right)+5}{2}=\dfrac{37}{2} \\
 & \Rightarrow \dfrac{4y+5}{2}=\dfrac{37}{2} \\
\end{align}$
In the above equation we have common denominators, so we can equate the values in the numerator, then we will get
$4y+5=37$
Now subtracting the value $5$ from the above equation, then we will have
$4y+5-5=37-5$
 We know that $a-a=0$, then
$4y=32$
Dividing the above equation with $4$, then we will get
$\begin{align}
  & \dfrac{4y}{4}=\dfrac{32}{4} \\
 & \Rightarrow y=8 \\
\end{align}$
$\therefore $ From the both methods we got the value of $y$ as $8$.