How do you solve for $x:{\text{ }}\left( {3x - 3} \right) = 12$?

Hint: In this question, we want to solve the linear equation of one variable. A linear equation of one variable can be written in the form $ax + b = c$. Here, a, b, and c are constants. And the exponent on the variable of the linear equation is always 1. To solve the linear equation, we have to remember that addition and subtraction are the inverse operations of each other. For example, if we have a number that is being added that we need to move to the other side of the equation, then we would subtract it from both sides of that equation.

Complete step by step solution:
In this question, we want to solve the linear equation of one variable.
The given equation is,
$ \Rightarrow 3x - 3 = 12$
Let us solve this equation,
First, we will add 3 on both sides.
That is equal to,
$ \Rightarrow 3x - 3 + 3 = 12 + 3$
Let us apply addition on both sides. The addition of 3 and -3 is equal to 0 on the left-hand side, and the addition of 12 and 3 is equal to 15 on the right-hand side.
Therefore,
$ \Rightarrow 3x = 15$
Now, let us divide by 3 into both sides.
$ \Rightarrow \dfrac{{3x}}{3} = \dfrac{{15}}{3}$
Let us apply addition on both sides. The division of 3x and 3 is equal to x on the left-hand side, and the subtraction of 15 and 3 is equal to 5 on the right-hand side.
Therefore,
$ \Rightarrow x = 5$

Hence, the solution of the given equation is 5.

Note:
Let us verify the answer.
$ \Rightarrow 3x - 3 = 12$
Let us substitute the value of x is equal to -2 in the above equation.
$ \Rightarrow 3\left( 5 \right) - 3 = 12$
That is equal to,
$ \Rightarrow 15 - 3 = 12$
Let us apply subtraction on the left-hand sides.
$ \Rightarrow 12 = 12$
Hence, the answer we get is correct.