 This video is about absolute value applications. So in order to satisfy college control, the marble columns of a company produces a stress test score of S that satisfies the inequality S minus 17,750 is less than or equal to 275. So we want to solve the inequality. So let's do that first. So to solve the inequality remember we're just going to drop the inequality and just say S minus 17,750 is going to be less than or equal to 275. But we also have to look at the S minus the 17,50 could possibly be a negative value. So it's a negative 275, but remember it's kind of like we multiplied this side by negative one so we have to switch the inequality. So if I add 17,750 to the 275 we're going to get S to be less than or equal to 18,025. And if we add it to the negative 275, S is going to be greater than or equal to 17,475. And then the question says determine if a score of 17,500 is in the passing range. 17,500 is greater than that so yes it passes. For all recruits in the 3rd Armored Battalion the average number of sit ups is 125. For an individual recruit the amount varies by no more than 23 sit ups from the battalion average. Find the average. Well one of the things that's going to be important here is no more than. We know there's a difference of about 23 and that difference is the number of sit ups and the 125 that is the average. So we're going to make that the absolute value. No more than means it can be less than but not greater than. So less than but no more than implies that it can be equal to 23. So we have S minus 125 less than or equal to 23. And we also have S minus 125 is greater than or equal to the opposite or negative 23. Switch to inequality gave it a negative. So if I add 125 to 23 we're going to have 148 which is S is less than or equal to 148. And if we add 125 to negative 23 we're going to have S is greater than 102. And so we would say that the range is between 102 and it includes it because the inequality includes it up to 148.