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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!
• 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!
• 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.
• 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.
• The ones in the exercise are a lot more difficult. The wording really throws everything off.
• 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.
• Adding x + (x+2) + (x+4) with x = lowest number
3x +6 > 100 thus, 3x > 94 which gives x > 31 +1/3
so x has to be the next odd number > 31 + 1/3 or 33
• 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?
• 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.
• 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.
• Great chart! You are a great explainer!
• 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?
• You only switch the sign when you are either multiplying or dividing by a negative number. It doesn't matter with addition or subtraction.
• 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?
• 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