yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Analyzing structure with linear inequalities: balls | High School Math | Khan Academy


2m read
·Nov 11, 2024

A bag has more green balls than blue balls, and there is at least one blue ball. Let B represent the number of blue balls, and let G represent the number of green balls. Let's compare the expressions 2B and B + G. Which statement is correct?

So, they make a bunch of comparisons between 2B and B plus G: is it greater than, less than, equal, or is there just not enough information to tell? And so, like always, pause this video and see if you can figure it out on your own before we work through it together.

All right, let's work through it together, and let's see what information they are giving us. So, this first sentence says a bag has more green balls than blue balls. We can translate that in math language as "the number of green balls is greater than the number of blue balls." It also says there is at least one blue ball. So, just translating that mathematically, we know that B is going to be greater than or equal to 1. There is at least one, but maybe more, so B is greater than or equal to one.

Now, let's see if we can somehow manipulate these so we can get to some reasonable sense of how B + G compares to 2B. Well, there are a bunch of different ways that you could approach it, and you might find a way to approach it that is different from my way. But the one that jumps out at me is, well, I know that G is greater than B. If I add a B to both sides on the left-hand side, I'm going to have B + G, and on the right-hand side, I'm going to have B + B. This right over here is 2B.

So, just like that, I know I can keep the inequality if I'm doing the same thing to both sides. If I'm adding or subtracting the same thing to both sides, just from G is greater than B, if you add B to both sides of that, we can deduce that B + G is going to be greater than B + B, or it's just going to be greater than 2B.

And that's all we need to do. Let's see which of these choices match up to that. So, let’s see: all of these have 2B on the left-hand side, so we could rewrite this as 2B is less than B + G, and that is that choice right over there.

More Articles

View All
The Big Misconception About Electricity
This video was sponsored by Caséta by Lutron. Imagine you have a giant circuit consisting of a battery, a switch, a light bulb, and two wires, which are each 300,000 kilometers long. That is the distance light travels in one second. So, they would reach o…
Amputee Skier Shreds Expectations | Short Film Showcase
His talent pretty much exceeds most any skier I’ve ever seen. He got just to be this incredible, incredible skier. It’s impressive. Vu is probably the best athlete I’ve seen and worked with. I do forget that he has, he has got the one leg. My name is Bas…
The Future of Driving | Years of Living Dangerously
TY BURRELL: Now that I’ve learned self-driving cars aren’t that far off, what about ride sharing? Are companies like Lyft and Uber going to be part of the solution? How you doing? All right? What are the odds? You are John Zimmer, President of Lyft. You g…
Descendents of Cahokia | Podcast | Overheard at National Geographic
Tucked away in St. Louis, Missouri, in a southern section of the city, just between the Mississippi River and Interstate 55, there’s a historic landmark, but you’d never know it. It’s on a road that’s easy to miss and, frankly, pretty beat up. There’s not…
Dostoevsky - Walk Your Own Path, Face Your Errors
In Crime and Punishment, Fyodor Dostoevsky wrote, “That’s man’s one privilege over all creation. Through error you come to the truth! I am a man because I err! You never reach any truth without making fourteen mistakes and very likely a hundred and fourte…
2d curl intuition
Hello everyone! So I’m going to start talking about curl. Curl is one of those very cool vector calculus concepts, and you’ll be pretty happy that you’ve learned it once you have it, for no other reason than because it’s kind of artistically pleasing. Th…