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## Modeling with linear inequalities

# Writing two-variable inequalities word problem

CCSS.Math:

## Video transcript

- [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.