Question

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

Answer 1

Hint: We will first take the least common multiple on the left hand side and then keep on doing the required simplifications and calculations to get the value of x.

Complete step-by-step answer:
We are given that we are required to solve $\dfrac{1}{5} + \dfrac{1}{x} = \dfrac{1}{2}$.
First of all, we will take the least common multiple on the left hand side to obtain the following expression:-
$ \Rightarrow \dfrac{{x + 5}}{{5x}} = \dfrac{1}{2}$
Now, cross – multiplying both the sides, we will then obtain:-
$ \Rightarrow $2 (x + 5) = 5x
Now, opening the bracket on the left hand side, we will then obtain:-
$ \Rightarrow $2x + 10 = 5x
Bringing the 5x from addition in right hand side to subtraction in left hand side, we will then get:-
$ \Rightarrow $2x – 5x + 10 = 0
Taking 10 from addition in the left hand side to subtraction in the right hand side to obtain the following expression:-
$ \Rightarrow $2x – 5x = - 10
Now, doing the calculations by clubbing the terms on the left hand side, we will then obtain the following equation:-
$ \Rightarrow $– 3x = - 10
Since on the both sides, we have negative sign, we can cancel them out to get the following equation:-
$ \Rightarrow $3x = 10
Now, dividing both of the sides of above equation by 3, we will then obtain the following equation:-

$ \Rightarrow x = \dfrac{{10}}{3}$
Hence, we have the required value of x.

Note:
The students must note that here we have one equation and only one variable that is x, thus we could solve it for x. We need as many equations as many numbers of variables we have. Here, we had one, so we found it using the given equation.
The students must note that there is an alternate way to do the same:-
We are given that we are required to solve $\dfrac{1}{5} + \dfrac{1}{x} = \dfrac{1}{2}$.
First of all, we will take $\dfrac{1}{5}$ from addition in the left hand side to subtraction in the right hand side. We will then get:-
$ \Rightarrow \dfrac{1}{x} = \dfrac{1}{2} - \dfrac{1}{5}$
Now, we will take the least common multiple on the right hand side to obtain the following expression:-
$ \Rightarrow \dfrac{1}{x} = \dfrac{{5 - 2}}{{10}}$
Simplifying it and taking reciprocal of both the sides, we will get:-
$ \Rightarrow x = \dfrac{{10}}{3}$
Hence, we have the required value of x.