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### Course: Operations and Algebraic Thinking 222-226>Unit 2

Lesson 8: Two-step inequalities

# Two-step inequality word problem: apples

We'll talk you through this fun and challenging inequality problem. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• I still don't get what an inequality is too well. I'm sorry, but can someone explain?
• I'm assuming that, since you are currently studying inequalities, that you've probably already done some basic study on the equation, and as you most likely already know, and equation states that one side is equal to another.

If I have the very simple equation X = 8, it is saying that X is equal with the other side of the equation, which is just 8. That is pretty simple, right? X just has 8 in it to make it equal with the other side. Most people don't really have to think too hard to know that X is just 8 in this case.

Well, an inequality is just the opposite. It states that the sides ARE NOT equal, and shows how. What if we saw X < 8? This says that whatever is in X is LESS THAN 8. It cannot be equal to 8, because the inequality says that it is less than 8.

Or if we were to see X > 8, we would know that whatever was in X was more than 8. That's important because the inequality says that whatever X has will be more than 8, so to make this inequality "true", so to speak, X has to be greater than 8. If we stick 7 into it, for instance, we would end up with 7 > 8, which of course is FALSE.

What about X >= 8, though? (If you see this in textbooks, you'll actually see a little more-than symbol with a line under it instead of a more than sign and an equals sign. It is the same thing, however. )

Anyway, >= is basically the same thing as the > symbol, except that in the > symbol, only numbers that are GREATER will make it true, but in the >= symbol, numbers that are greater will make it true, but numbers that are equal will ALSO make it true, which is why we also see the equals sign. It is the more-than-or-equal-to sign.

Is 8 >= 8 true? Well, 8 is equal to 8, so yes, this is true, since the >= will have the inequality true when both sides are equal, or when the left side is more than the right side. In either of these cases, the inequality is true, so this is TRUE.

Is 10>=8 true? Well, 10 is more than 8, so yes it is!

7 >= 8 true? No, it is not, since 7 is less than 8, which will not make this true. So this is FALSE.

Or what about the <= symbol? Well, this is the same thing, except only numbers that are less than, or equal, will make it true. It is the less-than-or-equal-to symbol. (Again, in textbooks, you'll see this symbol as a normal less-than symbol, but with a little line under it. The <= thing is used on computers to make it easier to type, so that's why you see it like that. )

is 9 <= 8 true? No, it is not, since 9 is more than 8.

Is 7 <= 8 true? Yes, 7 is less than 8, so this is true.

is 8 <= 8 true? Well, since 8 is equal to 8, this is true.

I hope that this helps! I know this isn't really all that detailed as how to solve them, but I hope that this is still helpful in at least understanding how they relate to equations.
• at it says multiply both by 2/3 cant you just divide both by 3 and then multiply them by 2?
• Yes you can but that's the same thing as multiplying both sides by 2/3.
Because 2*1/3 = 2 divided 3 = 2/3
• So if it says that Old Maple Farms has EXACTLY 1000 more apples than River Orchards
does this whole thing become an equality statement? like;
M = R + 1000
M/3 = (R + 1000)/3
M/3 + x = (R + 1000)/3 + x
or am i missing something?
• You are correct, it becomes an equality statement. And no, you're not missing something.
• what is the difference between equation and inequalities
• An equation has an equal sign, inequalities have a less than, greater than, less then or equal to, or greater than or equal to sign.
• I think i understood but where in life will this be usable?
• An individual must know quite a bit of math to be a, Doctor , Chemical Engineer , Electronic Engineer , M B A , Astronomist , Physicist , Geologist , Astonaut , Economist , Cosmologist , etc.
• who here was forced to do this.
• me. I got to do this for grade recovery
(1 vote)
• I'm just wondering why the A isn't deducted from the equation since it's the same on both sides. Thereby leaving the original 2/3M > 2/3R. I could understand the extra steps if the increases were different, but this seems like extra steps for the sake of extra steps. Mind you, I am refreshing after 30+ years out of Alg 1 &2.
• Having it as M > R also serves the same purpose because 2/3 didn't change the inequality either.

But i think its to show the steps and how we actually reach to that conclusion by working it out.
• At s, Sal says that "going down by a 1/3 is the same as multiplying by 2/3". If I want to verify this, how can I do that? I seem to have a problem understanding ratios, it's really frustrating (especially with fractions).
• I don't see how that's possible either, except for the number 1... He must not be talking about regular numbers. Maybe he meant X minus one-third X = two thirds X... I checked it out and yes that does work. Maybe he made a mistake in his video. But I'm pretty sure he mean X minus one-third X = two thirds X.

If you have anymore questions, ask me. :D