Question

What is the solution set of the equation $\dfrac{x}{5}+\dfrac{x}{2}=14$?

Answer 1

Hint: To obtain the solution of the equation given use LCM method. Firstly take LCM of the two terms in the denominator and then multiply each fraction with a term so that the denominator becomes equal to the LCM then add the numerator terms and simplify the equation obtained to get the solution.

Complete step by step answer:
The equation is given as:
$\dfrac{x}{5}+\dfrac{x}{2}=14$…..$\left( 1 \right)$
Now firstly we will find the LCM of the denominator value by using common division method as below:
$\begin{align}
  & 2\left| \!{\underline {\,
  5,2 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5,1 \,}} \right. \\
 & 1,1 \\
\end{align}$
The factors obtained are:
$\left\{ 2,5 \right\}$
So the LCM is:
$\begin{align}
  & \Rightarrow 2\times 5 \\
 & \Rightarrow 10 \\
\end{align}$
We got the LCM as 10.
Next, we will multiply and divide 2 and 5 in the first and second term of the left side of equation (1) respectively as:
$\begin{align}
  & \Rightarrow \dfrac{x}{5}\times \dfrac{2}{2}+\dfrac{x}{2}\times \dfrac{5}{5}=14 \\
 & \Rightarrow \dfrac{2x}{10}+\dfrac{5x}{10}=14 \\
\end{align}$
Now as the denominator of both the fraction is equal we can add the numerator as:
$\begin{align}
  & \Rightarrow \dfrac{2x+5x}{10}=14 \\
 & \therefore \dfrac{7x}{10}=14 \\
\end{align}$
Now we will simplify the above equation by keeping $x$ term on one side and taking all other terms on another side as:
$\begin{align}
  & \dfrac{7x}{10}=14 \\
 & \Rightarrow x=14\times \dfrac{10}{7} \\
 & \Rightarrow x=2\times 10 \\
 & \therefore x=20 \\
\end{align}$
So we got the value of $x$ as 20.

Hence solution of equation $\dfrac{x}{5}+\dfrac{x}{2}=14$ is $x=20$

Note: A equation is a mathematical expression that has two equal sides separated by an equal sign. A solution of an equation is the value that satisfies the equation. If we put the solution value in the equation we will get the left side equal to the right side. To check whether the solution obtained is correct or not we will put $x=20$ in the equation as:
$\begin{align}
  & \dfrac{x}{5}+\dfrac{x}{2}=14 \\
 & \Rightarrow \dfrac{20}{5}+\dfrac{20}{2}=14 \\
 & \Rightarrow 4+10=14 \\
 & \Rightarrow 14=14 \\
\end{align}$
As we can see, the right side is equal to the left side which means our solution is correct.