Question

How do you solve for y in M = 2x + 3y?

Answer 1

Hint: We will first of all take the terms with y on the left hand side and other terms on the right hand side, now we will divide by such a constant that we have only y in left hand thus do the required modifications.

Complete step-by-step solution:
We are given that we are required to solve for y in M = 2x + 3y.
Now, we will take 3y from addition in the right hand side to subtraction in the left hand side to obtain the following equation:-
$ \Rightarrow M – 3y = 2x$
Now, we will take M from addition in the left hand side of the above equation to subtraction in the right hand side of the above equation to obtain the following equation:-
$ \Rightarrow – 3y = 2x – M$
Now, we multiply the both sides of the above equation to obtain the following equation:-
$ \Rightarrow 3y = - 2x + M$
Now, we will divide the whole equation in the above line by 3 to obtain the following expression:-
$ \Rightarrow \dfrac{{3y}}{3} = \dfrac{{ - 2x + M}}{3}$
Simplifying the left hand side and the right hand side of the above equation, we will then obtain the following equation:-
$ \Rightarrow y = \dfrac{{ - 2x}}{3} + \dfrac{M}{3}$
Thus, we have obtained the required.

Note: The students must note that we have used the fact that: $\dfrac{{a + b}}{c} = \dfrac{a}{c} + \dfrac{b}{c}$ by putting a = -2x, b = M and c = 3 in the last step.
The students must also note that we can only multiply or divide by a number which is non – zero like here we divided the whole equation by 3 because we know that 3 is not equal to 0.
The students must also note that if we have an inequality and we multiply the equation by negative sign, then we always reverse the sign but here we had an equality, so it did not change anything.