Solve the equation $2x-5=3\left( x-5 \right)$ for the value of x.

Hint: Here, we will solve the given linear equation by taking all the terms containing x to one side and the constant terms to the other side. In this way, we can get the value of x.

Complete step-by-step answer:

The equation given to us in this problem is a linear equation in one variable. A linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two constants and x is variable and has only one solution. Linear equations are solved using basic algebraic operations. Linear equations are classified into three types that are- identity, conditional or inconsistent. An identity is true for all values of the variables. A conditional is true only for certain values of variables. An inconsistent equation is a false statement that is, it is not true for any value of variables.

The linear equation given to us here is $2x-5=3\left( x-5 \right)$. This equation must be conditional or identity to have a solution.

But this is not an identity equation. So, it is a conditional linear equation. We can write this equation as:

$\begin{align}

  & 2x-3x=-15+5 \\

 & \Rightarrow -x=-10 \\

\end{align}$

On multiplying both sides by -1, we get:

$\begin{align}

  & \left( -1 \right)\times \left( -x \right)=-1\times \left( -10 \right) \\

 & \Rightarrow x=10 \\

\end{align}$

So, the value of x comes out to be 10.

Hence, the solution of the given linear equation is x = 10.

Note: Students should note here that since the number of solutions of any equation depends on the number of variables in the equation. The equation given here has only one variable, so it has only one solution.