How do you solve $\dfrac{{3x}}{5} = x - 1$?

Hint: In order to determine the value of variable $x$ in the above equation, first multiply both sides with the number $5$and use the rules of transposing terms to transpose terms having $(x)$ on the Left-hand side and constant value terms on the Right-Hand side of the equation. Solving like terms and dividing both sides with the coefficient of variable x to get your desired solution.

Complete step-by-step solution:
We are given a linear equation in one variable $\dfrac{{3x}}{5} = x - 1$.and we have to solve this equation for variable ($x$).
$ \Rightarrow \dfrac{{3x}}{5} = x - 1$
Multiplying both sides of the equation with the number $5$, we get
$
   \Rightarrow 5\left( {\dfrac{{3x}}{5}} \right) = 5\left( {x - 1} \right) \\
   \Rightarrow 3x = 5x - 5 \\
 $
Now combining like terms on both of the sides. Terms having $x$will on the Left-Hand side of the equation and constant terms on the right-hand side.

Let’s recall one basic property of transposing terms that on transposing any term from one side to another the sign of that term gets reversed .In our case,$5x$ on the right hand side will become $ - 5x$ on the right hand side .
After transposing terms our equation becomes
$
   \Rightarrow 3x - 5x = - 5 \\
   \Rightarrow - 2x = - 5 \\
 $
Now dividing both sides of the with the coefficient of x i.e. $ - 2$
$
   \Rightarrow \dfrac{1}{{ - 2}}\left( { - 2x} \right) = \dfrac{1}{{ - 2}}\left( { - 5} \right) \\
   \Rightarrow x = \dfrac{5}{2} \\
 $
Therefore, the solution to the equation $\dfrac{{3x}}{5} = x - 1$is equal to $x = \dfrac{5}{2}$.

Additional Information: Linear Equation: A linear equation is a equation which can be represented in the form of $ax + c$where $x$ is the unknown variable and a,c are the numbers known where $a \ne 0$.If $a = 0$then the equation will become constant value and will no more be a linear equation. The degree of the variable in the linear equation is of the order 1. Every Linear equation has 1 root.

Note:
1. One must be careful while calculating the answer as calculation error may come.
2.There is only one value of x which is the solution to the equation and if we put this x in the equation, the equation will be zero.