 So let's take a look at problem 3.5, and again, don't watch this video. Remember a main goal of our course is to develop your problem-solving opportunity, and you only ever have one opportunity to solve a problem. If somebody shows you how to solve the problem, you will never ever again have the opportunity to solve that type of problem. So this particular video explains how to solve the problem of finding zero minus five, but the instant that you finish it, forever after, anything similar is not going to be a problem. Zero minus eight. This is not a problem because you will know how to find it. And again, after you watch this video, you will never again have the opportunity to solve this problem of finding zero minus eight. And again, problem-solving opportunities are extremely rare, so you have to ask yourself, are you ready to lose forever an educational opportunity? Your education will be worse after you watch this video because you will have given up a portion of it. All right, so assuming that we're ready to give up a part of our education, let's go ahead and tackle this problem. So let's zero minus five equal x, and we want to find this zero minus five using our various properties and definitions. So let's take a look at that. So first off, our definition of subtraction, well, that's a subtraction. We go look up our definition of subtraction, and a subtraction says that any time I have a subtraction, I also have an addition. Our definition of subtraction tells us that this and this are tied together. So by the definition of subtraction, I know that zero minus five equals x is the same as zero is equal to x plus five. Well, now here's something that's worth noting. Again, pulling our definitions, I have the sum of two things gives me zero. Well, my definition of additive inverse says that if I have two things that add to zero, they have to be additive inverses of each other. So that tells me that x is equal to the additive inverse of five. x is negative five in common language. Now let's see if we can generalize that. Well, I can apply exactly the same logic to anything zero minus a. Zero minus a, whatever it is, well, that tells me that zero and x plus a have to be the same thing, and that means that I have to have the additive inverse of whatever a is. And so in general, when I look at zero minus a, it's got to be the additive inverse of a.