How do you solve $\dfrac{6}{7x}=\dfrac{4}{5x-1}$?

Hint: In this question by solving the given equation we have to find the value of an unknown variable. To solve this question first we will cross multiply the terms. Then by solving the addition, multiplication, subtraction or division obtained in the equations we will find the value of an unknown variable i.e. x.

Complete step-by-step solution:
We have been given an expression $\dfrac{6}{7x}=\dfrac{4}{5x-1}$.
We have to solve the given equation.
Now, to solve the given expression first let us cross multiply the terms. Then we will get
$\Rightarrow 6\left( 5x-1 \right)=4\times 7x$
Now, simplifying the above obtained equation we will get
$\Rightarrow 30x-6=28x$
Now, shifting the variable term to the LHS and shifting the constant term to the RHS of the equation we will get
$\Rightarrow 30x-28x=6$
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow 2x=6 \\
 & \Rightarrow x=\dfrac{6}{2} \\
 & \Rightarrow x=3 \\
\end{align}$
Hence by solving the given equation we will get the value of x as 3.

Note: The point to be noted is that when the terms are moved from left to right or from right to left, the negative sign becomes positive and the positive sign changes to negative. So be careful while moving the terms and avoid calculation mistakes. We can also verify the answer by substituting the obtained value in the given equation. If we get the LHS and RHS equal after simplifying the equations then the obtained answer is correct.