Question

How do we solve for $x$ : $\dfrac{x}{3} = 12$ ?

Answer 1

The given equation is related to the linear equation of inverse operations. And the inverse operations are helpful for solving with respect to a variable. And, we will discuss first the whole procedure of how to find the value of $x$ or any variable. Then, on the procedure pattern, we will solve our given equation.

Step by step solution:-
Firstly, we will mention the whole procedure to find the values of $x$ is as follows:

Step-1: In the first step, we should keep variables in the left side and the constant values in the right side of the equation.

Step-2: Then solve the group of variables and constants separately in both the sides one by one like addition, subtraction, multiplication or division.

Step-3: Finally, both sides have one particular value of variables and constant, and we will solve that equation by sending the constant value of the variable of L.H.S with the constant of R.H.S, that’s how we will get our value of variable or $x$ .

Now, on this pattern we will solve the given equation, which is $\dfrac{x}{3} = 12$ :

First, we have to cancel out the $\dfrac{x}{3}$ to get a single $x$ .

To get $x$ from $\dfrac{x}{3}$ , we have to multiply $\dfrac{x}{3}$ by 3.

This action $( \times 3)$ needs to be completed on both sides of the equal sign.

So,
$\dfrac{x}{3} = 12$
$\Rightarrow \dfrac{x}{3} \times 3 = 12 \times 3$ (multiplying both sides by 3 to get the single $x$ )
$\therefore x = 36$

Note:- For cross checking our final value of $x$ , we will again substitute the solution for the variable in the real equation and see if both sides of the equation are equal or not:

$\dfrac{{36}}{3} = 12$ (substitute 36 in the place of $x$ )

$\Rightarrow 12 = 12$ (we get 12 in L.H.S by dividing 36 by 12)

So, after cross-checking, both sides are equal.