Question

Solve: \[\dfrac{8}{x} = \dfrac{5}{{x - 1}}\]

Answer 1

Hint: Here we are asked to solve the given equation to find the value of \[x\]. This can be done by using the transposition method. In this method, the unknown variable will be kept alone on one side of the equation and the other terms will be transferred to the other side. Then by evaluating the other side we will get the value of the unknown variable.

Complete step by step answer:
It is given that \[\dfrac{8}{x} = \dfrac{5}{{x - 1}}\] we aim to find the value of the unknown variable by solving this equation.
A simple equation can be solved by three methods one of the most efficient methods is the transposition method. In this method, we will try to keep the unknown variable on one side of the equation and transfer the other terms to the other side. Then by calculating that side we will get the value of the unknown variable.
Consider the given equation \[\dfrac{8}{x} = \dfrac{5}{{x - 1}}\], let us first cross multiply the denominators on both sides to the other side.
\[\dfrac{8}{x} = \dfrac{5}{{x - 1}} \Rightarrow 8\left( {x - 1} \right) = 5x\]
Now let us multiply eight on the left-hand side with the term \[x - 1\].
\[ \Rightarrow 8x - 8 = 5x\]
By the rule of the transposition method, we need to keep the unknown variable on one side and other terms to the other side. So, let us interchange the sides of the terms \[5x\] and \[ - 8\].
\[ \Rightarrow 8x - 5x = 8\]
On simplifying the above equation, we get
\[ \Rightarrow 3x = 8\]
Now let us take term three to the other side we get
\[ \Rightarrow x = \dfrac{8}{3}\]
Thus, we have found the value of the unknown variable \[x\] as \[\dfrac{8}{3}\].

Note:
 In mathematics, a simple equation can be solved by using three methods: trial and error, systematic, and the transposition method. Here we have used the transposition method because it takes less time for calculation than the other two methods. Also, we can check whether our answer is correct or not by substituting the value of the unknown variable in the given equation, it satisfies the equation then the answer is correct.