Question

How do you solve $\dfrac{1}{5}+\dfrac{1}{x}=\dfrac{1}{2}$?

Answer 1

Hint: The above given question is in fraction form. Fractions represent equal parts of a whole or a collection or we can say when we divide a whole into equal parts, each part is a fraction of the whole. A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator. It tells the total divisible number of equal parts which are there in a collection.

Complete step by step solution:
Now the given question is $\dfrac{1}{5}+\dfrac{1}{x}=\dfrac{1}{2}$, here we have to find the value of $x$.
Now first subtract the above give equation by $\dfrac{1}{5}$ from both sides of the equation, we get$\Rightarrow \dfrac{-1}{5}+\dfrac{1}{5}+\dfrac{1}{x}=\dfrac{1}{2}-\dfrac{1}{5}$
$\Rightarrow \dfrac{1}{x}=\dfrac{1}{2}-\dfrac{1}{5}$
Now taking LCM of $\left( 2,5 \right)$ and then solving the above equation we get
$\begin{align}
  & \Rightarrow \dfrac{1}{x}=\dfrac{5-2}{10} \\
 & \Rightarrow \dfrac{1}{x}=\dfrac{3}{10} \\
\end{align}$
Now reciprocal the both sides of the equation we get the value of $x$
$\Rightarrow x=\dfrac{10}{3}$
Since we need the value of $x$ in a fraction form so we will not simplify it.
Hence the value of $x$is $\dfrac{10}{3}$ in a fraction form.

Note: We can also check whether our value of $x$ is correct or not.
The given question is $\dfrac{1}{5}+\dfrac{1}{x}=\dfrac{1}{2}$
Now put the value of $x$ in this above equation we get
$\Rightarrow \dfrac{1}{5}+\dfrac{3}{10}=\dfrac{1}{2}$
Now solve the left part of the equation and it is equal to the right part or not.
Take the LCM of $\left( 5,10 \right)$ and then we get
$\Rightarrow \dfrac{2+3}{10}=\dfrac{5}{10}=\dfrac{1}{2}$
Now the left part of the equation becomes equal to the right part of the equation.
Hence our value of $x=\dfrac{10}{3}$ is correct.