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## Pre-algebra

### Course: Pre-algebra>Unit 10

Lesson 8: Two-step inequalities

# 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.

## Want to join the conversation?

• 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!
(9 votes)
• 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!
(13 votes)
• 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.
(4 votes)
• Run does mean points. However, the equation is 6+4p>17. (let p = points) Which would mean that 4p>11. And p would equal 11/4 points per inning, Round it up I made the mistake of rounding it down and got the question wrong.
(2 votes)
• 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.
(4 votes)
• Maybe itś because you don´t know how to spell wrong because you said i got it wrongly
(1 vote)
• 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.
(1 vote)
• Great chart! You are a great explainer!
(1 vote)
• 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?
(1 vote)
• You only switch the sign when you are either multiplying or dividing by a negative number. It doesn't matter with addition or subtraction.
(6 votes)
• 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)
• key thing in solving inequality word problem :-
at least - means greater than or equal to
no more than - means less than or equal to
more than - means greater than
less than - means less than
(6 votes)
• how do you know its greater than or equal to?
(2 votes)
• Sal explains that at in the video. The words "at least 120,000" mean you need to equal 120,000 or be higher than 120,000. So, use greater than or equal.
(2 votes)
• I will help you now that I´m in college!
(2 votes)
• Hi. I am really struggling to do the word problem practice. I can do this one in the video fine but when it gets to the practice I seem to be overcomplicating it. I have watched the videos and looked at the hints but still can't understand it? Like in the question

Tatiana wants to give friendship bracelets to her 32 classmates. She already has 5 bracelets, and she can buy more bracelets in packages of 4.
Write an inequality to determine the number of packages, p, Tatiana could buy to have enough bracelets.

My answer was, (32-5) over 4 is greater than or equal to p

When it should be 5+4p is greater than or equal to 32

I can't seem to understand it. Please help! Thanks, Hedgy2007
(2 votes)
• Uh wouldn't the problem be an equation? The correct answer is 42,000, if my math is correct. In my opinion, the inequality part is a liability
(2 votes)
• The words "at least 120,000" tells you to use and inequality of: ">= 120,000"
(1 vote)

## 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