Question

How do you solve $\dfrac{2}{3}x - 9 = 0$?

Answer 1

Hint: We will first take the constants to the right hand side and all the terms with variables on the left hand side. Then we will just do the modifications to get the value of the variable.

Complete step-by-step solution:
We are given that we are required to solve $\dfrac{2}{3}x - 9 = 0$.
Since, we see that it has a constant term of 9 in subtraction in the left hand side.
Taking 9 from subtraction in the left hand side to addition in the right hand side, we will then obtain the following equation with us:-
$ \Rightarrow \dfrac{2}{3}x = 9$
Since, we can clearly observe that there is a 3 in the denominator of the left hand side of the above equation, therefore, multiplying the both sides of above equation by 3, we will then obtain the following equation with us:-
$ \Rightarrow \dfrac{2}{3} \times 3 \times x = 9 \times 3$
Simplifying the left hand side of the above equation, we will then obtain the following equation with us:-
$ \Rightarrow 2x = 9 \times 3$
Simplifying the right hand side of the above equation, we will then obtain the following equation with us:-
$ \Rightarrow 2x = 27$
Since, we can clearly observe that there is a 2 in the numerator of the left hand side of the above equation, therefore, dividing the both sides of above equation by 2, we will then obtain the following equation:-
$ \Rightarrow x = \dfrac{{27}}{2}$

Hence, $x = \dfrac{{27}}{2}$ is the required answer.

Note: The students must note that whenever solving linear equations in one variable, you must always try to collect all the variables on the left hand side and all the constants on the right hand side, so that we have a clear equation and all the like terms on each side.
The students must also keep in mind that we cannot multiply or divide an equation by any such number which has any possibility of being 0.