Modeling with linear inequalities
- [Voiceover] Fabiano wants to score at least 6.5 points in a major chess tournament. He scores one point for each game that he wins, and he scores 0.5 points for each game that ends in a draw. Write an inequality that represents the number of games Fabiano should win and draw, D, to achieve his goal. So I encourage you to pause the video and see if you can do that. Write an inequality in terms of the number of games won, so capital "W", and the number of draws, capital "D", that represents what he needs to do to actually achieve his goal. All right, let's work through it together. So how many points he is going to get from winning? So if he wins "W", he's gonna win W games, and he gets one point for each of them, so it's gonna be one point per game, times the number of games. So one W I could just write as W. So this is the points from winning. From wins, I could say. And what are his points gonna be from the draws? Well, from the draws, he's gonna have D draws, and he gets 0.5 points for each of them. zero point five times D, this is going to be the points from the draws. Now, this right over here is going to be his total points, points from wins, points from draws. I'm assuming he gets no points for losses. And we want this number, the total number of points, his score, to be at least 6.5. So we want this to be greater than or equal to 6.5. If it says Fabiano wants to score more than 6.5, then it would have been greater than. But it says Fabiano wants to score at least 6.5, so that's greater than or equal to 6.5. He's ok if he scores 6.5. And there you have it, we have our inequality in terms of the number of games he needs to win and draw and this inequality needs to be true in order for him to score at least six and a half points in this major chess tournament.