Solving and Graphing Compound Inequalities - Problem 1
A compound inequality contains at least two inequalities. If the information on the word problem can be linked with an "and", write the inequality as a single line with two inequality signs. If the information can be linked with an "or", write two separate inequalities.
Any of you who have tried wrestling someone who's a lot bigger than you or a lot smaller than you, knows that it's really hard. So what happens in the United States is that boys are grouped into other boys of similar weight classes. So for example we have this problem that's going to ask us to use a compound inequality, let's just do it.
In the Unites States, high school boys wrestling, one weight class is greater than 103 pounds but not exceeding 112 pounds. Write a compound inequality to show the weights that are within this range.
So what this means is that any guy who comes out for wrestling who weighs 113 pounds gets in this class. If he weighs, no he doesn't he gets in the next class, my fault. If he weighs 111 pounds, he's in this class. If he weighs 113 pounds he's going to be in the other class.
The tricky stuff comes with what if he weighs 112 pounds exactly, like 112.0. We have to write a compound inequality to describe this.
Well let's see we know the lower number is 103 pounds, we know the higher number is 112 pounds and we want to stick x, x representing the boys weight in the middle. Let's see it has to be greater than 103 pounds so that's how I'm going to mark it. X has to be greater than 103 pounds. And then he cannot exceed 112, he can be 112 exactly but he can't be 112.1 that's the tricky part and that's why a compounded inequality can be really useful.
So this is our final answer x is the number that has to be greater than 103 but x can be less than or equal to 112. This is something that shows up in real life like I want you guys to hopefully understand that Math really is a part of real life. This is the place where they use it in wrestling.