Question

How do you solve $\dfrac{1}{x}=3.5$ ?

Answer 1

In this question, we need to find the value of x. As we see, the equation consists of a variable and a decimal number. So, to solve this problem we first change the decimal number into a fraction by multiplying and divide the right-hand side of the equation by 10, then remove the decimal number. After that, we do the necessary calculations and take the reciprocal on both sides of the equation. Then, we see that the fraction on the right-hand side of the new equation has a common factor 5, so we make further calculations to get the value of x, which is our required answer.

Complete answer:
According to the question, we have to find the value of x.
The equation given to us is $\dfrac{1}{x}=3.5$ ----------- (1)
So, we first multiply and divide 10 on the right-hand side in the equation (1), we get
$\Rightarrow \dfrac{1}{x}=(3.5).\dfrac{10}{10}$
Now, we remove the decimal point, we get
$\Rightarrow \dfrac{1}{x}=\left( \dfrac{(35)}{10} \right).\dfrac{10}{10}$
On further simplification, we get
$\Rightarrow \dfrac{1}{x}=\left( \dfrac{35}{10} \right)$
Now, take the reciprocal of both the sides of the above equation, we get
$\Rightarrow x=\left( \dfrac{10}{35} \right)$
Thus, $\dfrac{10}{35}$ have a common factor 5, thus new equation we get
$\Rightarrow x=\dfrac{2}{7}$
Therefore, the value of x for the equation $\dfrac{1}{x}=3.5$ is $\dfrac{2}{7}$.

Note: Make all calculations properly and avoid mistakes by doing each step properly. Do not forget to remove the decimal point and always take reciprocal because x lies in the denominator. One of the alternative methods to solve this problem is to cross multiply both the side of the equation and then remove the decimal point and make necessary calculations, to get the value of x, which is our required answer.