What is presented here is an example of a two-column proof, where one side lists the steps in the order in which the author worked and the parallel side explaining the reason behind each step. In the first example, it shows that the equation is given because we did not need any sort of thinking to come to the conclusion that 2/3y +15 = 9. The second step is actually Subtraction of Equality because we are subtracting the integer 15 from both sides, therefore both sides are still equal.
In the third step, the reason provided is simplification. We can infer that this means we will need to combine like terms since the step before has like terms (15 and -15, 9 and -15). If we combine these terms we get 2/3y = -6.
The fourth step of action we can probably take from step three, is to multiply both sides by 3 in order to eliminate the denominator. With that we get, 2y = -18 and can be justified by simplification. The final step calls for simplification, meaning all we have to do is either add, subtract, divide, or multiply both sides by the same number. We are solving for y, so in order to get y alone we must divide both sides by 2. This is to get rid of any coefficient of the y variable. The final step of this proof is y = -9 Hope this helps!
