Question

Given \[k=a+3mx\] how do you solve for \[m\]?

Answer 1

Hint: From the question we have been asked to find the value of \[m\]. To solve the questions of this kind we will bring the terms other than \[m\] to one side and make the \[m\] as subject. After doing that we will use the basic operation in mathematics which is division and reduce or simplify the solution. So, we will proceed as follows.

Complete step by step answer:
Firstly, for the given question we will bring the term a to the left hand side of the equation. So, the equation will be reduced as follows.
\[\Rightarrow k=a+3mx\]
\[\Rightarrow k-a=3mx\]
Now, for the above equation we will use the basic operation in mathematics that is division and simplify the equation further.
Here for the above equation we will divide both the left hand side and the right hand side of the equation with \[3x\]. So, after doing it we get the equation reduced as follows.
\[\Rightarrow \dfrac{k-a}{3x}=\dfrac{3mx}{3x}\]
Now, for this equation we can observe that on the right hand side of the equation the term \[3x\] is common on the numerator and denominator. So, we can cancel that term in the equation.
So, the equation will be further reduced as follows.
\[\Rightarrow \dfrac{k-a}{3x}=\dfrac{3mx}{3x}\]
\[\Rightarrow \dfrac{k-a}{3x}=m\]
\[\Rightarrow m=\dfrac{k-a}{3x}\]

Therefore, the solution will be \[ m=\dfrac{k-a}{3x}\].

Note: Students must be very careful in doing the simplifications very accurately. Students must have good knowledge in the concept of division. In the simplification process students should not make mistakes like for example if we write the equation as \[k+a=3mx\] instead of \[ k-a=3mx\] in the first step then our whole solution will be wrong.