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Two-step inequality word problem: R&B

Let's tackle this word problem together. We'll interpret the information and then construct a linear inequality to solve it. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • leaf grey style avatar for user PinkPigtails
    White Fang posted a similar question dated two years ago, but the answer isn't what I am looking for.

    How will I know whether or not it is >=, <=, < or just >? That is where I keep getting my answers wrong when I am doing the practice pages and I can't seem to place my finger on what's going on.

    Thanks to anyone who helps!
    (11 votes)
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    • purple pi teal style avatar for user Ellen Wight
      When I learned this at school, my teacher told the class some key phrases to look for to determine which sign to use. For >=, some are "is at least" and "is no less than" (x>=5; x is at least 5). <= would be "no more than", "at most", or "up to" (x<=5; x is at most 5). < is "lower than", "fewer than" (x<5; x is fewer or less than 5). > is "greater than", "exceeds", and "more than" (x>5; x is greater than or exceeds 5). When determining what to use in a word problem, look for those phrases or look at each sign and see what makes the most sense for the situation based on those phrases. Hope this helps - comment with any questions you have!
      (17 votes)
  • duskpin ultimate style avatar for user Kathrin Beyer
    Have a problem with a question in "Interpreting and solving linear Inequalities" The question is:
    "Kim's softball team is playing in the championship game. They are losing by a score of 17 to 6. There are 4 innings to go. Kim wants to know how many runs her team needs per inning to win the game if the other team does not score."
    I don't know this game and I thought it's not important to answer the question, but it seems I'am wrong with that. I thought they need 12 points more to win (17-6+1), so they have to do 3 runs in every inning (whatever this is). I get it wrong, like I said. The first sentence in the hints is: "Kim's team already has 6 runs." I don't get it. Where in the question is the information, that they have 6 runs. I thought the 6 means the points they have. I need a hint I understand.
    (5 votes)
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  • leafers ultimate style avatar for user joshh
    The ones in the exercise are a lot more difficult. The wording really throws everything off.
    (7 votes)
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  • piceratops seed style avatar for user Wkis
    I have a question from my textbook which I got it wrongly and I don't know why.
    Here it is: The sum of 3 consecutive odd numbers is greater than 100. What is the minimum value of the smallest odd munber among them?
    I wrote an equation: x+x+2+x+4 greater than 100
    And my answer: 31 over 1 over 3 / 94/3
    But the corrext answer is 33.
    (5 votes)
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  • blobby green style avatar for user sdav09
    My solution was: L≥120000-(45000+33000) which seems fine.
    But I encountered a similar problem where my approach fails.
    My solution: p ≥ (620 - 450) / 37.4
    Their solution: 620 - 37.4p ≤ 450
    They both evaluate to the same decimal: p ≥ 4.545454... or 50/11
    But the unit test says I'm wrong. What gives?
    Is it just preferred formatting?
    (4 votes)
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    • area 52 blue style avatar for user 30oliver.pape
      I have been having this same problem myself.
      Although your answer is also correct, they want you to use their inequality.

      Renna pushes the elevator button, but the elevator does not move. The mass limit for the elevator is 450 kilograms, but Renna and her load of identical packages mass a total of 620 kg. Each package has a mass of 37.4 kg. 620-37.4p is less than or equal to 450 which means that with all the packages that she subtracts, the weight will be taken away from 620. I think you are all good with the rest, but p=5 because you can't take out 4.545454... packages from the load. 5 would be the answer.

      Hope this helps.
      (5 votes)
  • old spice man green style avatar for user Shin Andrei
    Are there any keywords to help me know if the inequality is greater than, less than, greater than or equal to or less than or equal to. I already know that: at least = greater than or equal and at most = less than or equal. Any keywords will be really helpful.
    (2 votes)
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  • aqualine ultimate style avatar for user adrianjayson13
    Sorry, I'm not sure if I'm missing something, but aren't you supposed to shift the signs from 'greater than or equal to' to 'less than or equal to' sign since we subtracted 78,000 from both sides?
    (2 votes)
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  • marcimus pink style avatar for user Kieran L*******
    45000+33000=78000
    120000-78000=42000
    The amount of people who watch the show in La-Vegas was equal to or less than 42000 people.

    Isn't that an easier way to do it?
    (0 votes)
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  • blobby green style avatar for user Sierra
    I wish he gave some harder examples. I feel like this video is easier than the exercise.
    (5 votes)
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  • starky seedling style avatar for user alyha.hawkins
    I will help you now that I´m in college!
    (4 votes)
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Video transcript

A popular R&B band recently returned from a successful three-city tour where they played to at least 120,000 people. My brain immediately says that's greater than or equal to 120,000. If they had an audience of 45,000 in Mesa and another 33,000 in Denver, how many people attended their show in Las Vegas? So let's say Las Vegas, I'll just use l for Las Vegas. So the number of people who attended their show in Las Vegas plus the number that attended their show in Mesa, which is 45,000, plus the number of people that attended their show in Denver, which is 33,000-- those are three cities right there, Las Vegas, Mesa, and Denver-- that has to be at least 120,000 people. Or another way of interpreting that is greater than or equal to 120,000. So to figure out how many people attended their show in Las Vegas, we just solve for l on this inequalty. So if we simplify this left-hand side, we get the number of people in Las Vegas plus-- what's 45,000 plus 33,000, that is 78,000-- 78,000 is going to be greater than or equal to 120,000. Now to isolate the l on the left-hand side of the inequality, we can subtract 78,000 from both sides. So minus 78,000, minus 78,000 on the left-hand side, these cancel out. And we're just left with the number of people who attended the show in Las Vegas is going to be greater than or equal to 120,000 minus 78,000. So 120,000 minus 80,000 is 40,000, and it's going to be another 2,000. So the number of people who attended Las Vegas is going to be greater than or equal to 42,000 people. And we're done, that's it