# JP4 SOLVING INEQUALITIES

This eighth grade mathematics lesson focuses on equations that are inequalities. It is the seventh lesson in a sequence of eight on this topic. The lesson is 50 minutes in duration. There are 34 students in the class.

TimeCaption
00:00:08Onegaishimasu.
00:00:09Onegaishimasu.
00:00:10Okay. Onegaishimasu.
00:00:15Okay, we're going to start our homework answer comparisons
00:00:18so, please take out handout number nine.
00:00:20Now I'll have you write it. Please write, right?
00:00:24Okay, it's this row.
00:00:25One, two, three, four, five, six.
00:00:28Okay, then please write it. Okay.
00:01:16I'm going to check it so those of you
00:01:18who haven't done it,
00:01:21please hurry and do it, okay?
00:01:29This... then.
00:01:47I will hold this microphone... and walk around.
00:01:50Okay.
00:01:51Okay, then I'm going to check it
00:01:53so please show it to me, okay? Okay.
00:01:55Okay. Oh, great.
00:01:58Everyone did their homework today
00:02:00because we're going to be on TV.
00:02:02Did you copy it?
00:02:06Just one person...
00:02:09just one person is a little different.
00:02:12Arai!
00:02:13This child... has forgotten his homework.
00:02:23Bancho, you could do it by yourself, right?
00:02:25Chino?
00:02:26Are you feeling better now?
00:02:28Okay. That's fine.
00:02:38Arai, please hurry and write it.
00:02:41It's only you, Arai.
00:03:11Okay. Okay, then I had you write six so...
00:03:15We'll compare answers together and verify them.
00:03:18Okay, number one.
00:03:20You exchange it and two X is less than 14.
00:03:23We divide both sides by two,
00:03:26so the inequality is X is less than seven.
00:03:29Number two. Transpose and
00:03:31negative five X is less than negative 10.
00:03:35Then you're dividing both sides by negative five
00:03:39so X is greater than or equal to negative two.
00:03:43Okay, then the third one.
00:03:52Multiply all with 10.
00:03:54Oh, you mean you multiplied 10, right?
00:03:58Okay. Ten- line up all of the head numbers
00:04:00and multiply them by 10,
00:04:02and 12 X minus four X is,
00:04:04it's already like this, right? Okay.
00:04:05Six and then 42.
00:04:06If you organize them like this,
00:04:08eight X is less than 48 and
00:04:11X is less than negative six.
00:04:13And number four is...
00:04:15take off the brackets and
00:04:17three X plus 12 is greater than five X plus two.
00:04:19Then you transpose, and
00:04:20negative two X is less than minus 10 and�when
00:04:22you divide both sides
00:04:24what is wrong at this point?
00:04:29Where is it wrong here?
00:04:31If I told you to correct it...
00:04:33where would you correct it?
00:04:39Eguchi, here... where should you correct it?
00:04:41How would you fix this?
00:04:43Number three and number nine.
00:04:45That problem is wrong.
00:04:50Teacher.
00:04:57Now it's okay, isn't it?
00:04:58Yes.
00:05:02Oh, negative two X.
00:05:04Yeah. At the negative two
00:05:05the inequality sign doesn't change yet.
00:05:07It's okay as it is. And
00:05:08when you divide it on both sides
00:05:09by negative two then the direction is changed
00:05:11to the opposite and X is less than five. Right?
00:05:13Huh? It doesn't change when it became negative two?
00:05:15Even if you combine like terms
00:05:17there is nothing that can change the inequality sign
00:05:20so just moving this one thing won't change it.
00:05:23This is written, so, this is here.
00:05:25So because this is here, its only at this point
00:05:27you change the direction, you know.
00:05:29You don't change it at the negative two part?
00:05:31Right. You don't change it at this point.
00:05:32You change the direction while you
00:05:33divide both sides with this denominator, you know.
00:05:35I didn't change it like that. Because this-
00:05:37this changes it to negative two.
00:05:39Because you do it with this.
00:05:40Write it like this and...
00:05:42I was too lazy to write that at the bottom.
00:05:44People who write it like this are okay.
00:05:46This corresponds. This is fine. Yes.
00:05:47It's just that there's this line and this line but...
00:05:49okay. Then number five. The brackets are removed.
00:05:52Negative six X is less than negative seven.
00:05:55Were there any strange points when you were doing it?
00:05:57Why does it end up as this kind of fraction?
00:05:59X greater than or equal to seven sixths?
00:06:01Correct.
00:06:02Okay, this is fine.
00:06:03There was one that became a fraction, right?
00:06:05Then the sixth one.
00:06:06It seems like it was multiplied by 10
00:06:08and was all calculated, but...
00:06:09You need to multiply 10 to this two as well
00:06:11and make it 20, so...
00:06:12Please be careful here because you may forget to write this.
00:06:15Then 13 X is greater than negative 13 and...
00:06:18X is greater than negative one.
00:06:21Then... four or more correct is good.
00:06:24It's a passing mark.
00:06:27Then...people who could do four or more.
00:06:29You are paper, okay?
00:06:31Then people who did less than four are rock, okay?
00:06:34One, two, and three!
00:06:38People who had four or more are paper, you know.
00:06:39People below four are rock.
00:06:41Arai has zero, right?
00:06:42Yes. It seems like everyone other than Arai is okay.
00:06:46Arai.
00:06:48Let's do our homework from now on, okay?
00:06:54Huh?
00:06:58Okay, then today will be the
00:07:01final part of the sentence problems so, then...
00:07:05I will have everyone use their heads and
00:07:07think a little, okay?
00:07:10Until now we've just done calculation practice,
00:07:12but today we will have to use your heads a little so...
00:07:15I'm asking you to use thinking methods.
00:07:16How to think and how to look for it and
00:07:18think about it may be a little difficult you know.
00:07:20More difficult than just simply calculating, that is. Right?
00:07:25Okay. Well then... please look at... the problem.
00:07:31Fukuda, can you see it?
00:07:32Yes?
00:07:33Can you see?
00:07:34I can see.
00:07:35You can see. Okay. Then, Genji.
00:07:43[ BB: Problem 3. You would like to buy 10 cakes all together for less than 2,100 yen. ]
00:07:44[ BB:One type of cake is 230 yen each and the other cakes are 200 yen each. ]
00:07:48You would like to buy 10 cakes all together
00:07:51for less than 2,100 yen.
00:07:54One type of cake is 230 yen each
00:07:57and the other cakes are 200 yen each.
00:07:59Yes.
00:08:00Do you understand the meaning of the problem?
00:08:04Arai, do you understand what this problem means?
00:08:07You have 230-yen cakes and 200-yen cakes, right?
00:08:10The 230-yen cakes are a bit more expensive.
00:08:12And... you have 10 family members.
00:08:15You want to buy cakes for each person.
00:08:18But, I have only 2,100 yen.
00:08:22Which cake... seems more delicious?
00:08:26The 230-yen one.
00:08:28The more expensive one is somehow more desirable, right?
00:08:30And so... you want to buy as many
00:08:33expensive cakes... as you can,
00:08:36but what's the maximum that you can buy?
00:08:41That's the problem.
00:08:44Understand?
00:08:45[ BB: If you want to buy as many 230-yen cakes as possible, what is the maximum number that you can buy? ]
00:08:46There are cakes that are 230 yen and 200 yen.
00:08:49You only have 210 yen.
00:08:51But you need to buy 10.
00:08:54But the 230-yen one looks more delicious
00:08:57so you want to buy as many as possible.
00:08:59Nine.
00:09:00But you only have 2,100 yen, so...
00:09:02so in fact how many 230-yen cakes can you buy?
00:09:07Nine.
00:09:08So today I am going to have you think about
00:09:15So now I will pass out paper,
00:09:20See, you can do it if you do it like this.
00:09:22See, you can understand- solve it if you do it like this.
00:09:24I will present the problem in this way, okay?
00:09:26Use the back, too. Four, five, six.
00:09:30Two, three, four, five, six.
00:09:32I didn't pass out the papers so... four, five, six, here.
00:09:35One, two, three, four, five, here.
00:09:38One, two, three, four, five, six.
00:09:42Three, four, five, six. Okay.
00:09:45I don't care about what kind of method you use
00:09:50Think about how many you could buy and how to figure it out.
00:09:54Do we solve this problem?
00:09:56This problem is for ninth graders,
00:09:58so you can't solve it, so please use the back.
00:10:00Please use back of the paper and think about it a little.
00:10:03What do you need to do in order to buy 230-yen cakes
00:10:06and up to how many can you buy and bring home?
00:10:13It's good if you come up with an answer,
00:10:20Well, we have about three minutes so it's okay
00:10:22if you do it while you write notes there.
00:10:23So, think about what you need to do to
00:10:25find out how many you can buy
00:10:28and find the answer. Okay, get started.
00:10:31Please work by yourself at first, okay?
00:10:34If you were in front of the store and you only had 210 yen
00:10:39Think about the time that you were in front of the store.
00:10:40What would you do?
00:10:45What?
00:10:49Then how are you going to think about it?
00:10:52That you can find it if you do such and such.
00:10:57[ BB: Way of thinking ]
00:10:59[ BB: Way of thinking ]
00:11:02Can you bargain and lower the price?
00:11:04Ordinarily they wouldn't bargain, would they?
00:11:07Although they might bargain if it
00:11:08were at a vegetable or fish store.
00:11:09I have never seen them bargain... at a cake store.
00:11:13They might have bargained if it were Kenchan's Cakes, right?
00:11:15Oh, don't you know it?
00:11:16Ah, I did it.
00:11:20for a while. About two minutes left.
00:11:21I told you not to use this but to use the back, didn't I?
00:11:30Because... what you really want is
00:11:32to buy 10 230-yen cakes, right?
00:11:36But if you buy 10 230-yen cakes how much will it cost?
00:11:38Two thousand three hundred yen.
00:11:39It'll end up being two thousand three hundred yen, right?
00:11:41However, you only have 2,000- 2,100 yen in cash so...
00:11:44You need to mix, mix it up or you can't buy it, you know?
00:11:47Because you only have 210 yen in cash.
00:11:49Then how do you need to think about it...
00:11:52in order to find out how many 230-yen cakes to buy?
00:12:00I don't care what kind of method you use.
00:12:02Inequality equation.
00:12:03Oh, if you want to set up an inequality equation
00:12:06If someone else says that they want to
00:12:07think about it with a different method
00:12:08because they don't need an inequality equation...
00:12:10That, that is fine for that person, too.
00:12:12I want to know how you think about it so...
00:12:19See... being asked to figure out
00:12:21how to think about it is more difficult
00:12:23than being asked to solve an equation, isn't it?
00:12:34Is it not permissible to buy nine?
00:12:36I don't get this.
00:12:59Don't get it?
00:13:01But, if you really were buying two kinds of cake
00:13:03you have to think about money,
00:13:04the money that you have and the bill.
00:13:06After you ask for the bill you can't say I'm sorry
00:13:09I want to return this. Can you?
00:13:11Then you exchange.
00:13:14That has happened to me a lot, too.
00:13:16I say oh, sorry! Please return this.
00:13:28How are you going to think about it?
00:13:38It's also okay if it's over 10, right?
00:13:43Ten?
00:13:49Ten.
00:13:50Ten.
00:13:51It's not 11 or 12 or eight, but buy exactly 10, okay?
00:13:57Well, then how can you... find out... how many you can buy?
00:14:02There are people who...would have them take the cake,
00:14:04take a 200-yen cake and break it in half
00:14:06and make it 100-yen.
00:14:07Okay, then you go to the cake store and
00:14:09try and request that.
00:14:10Most people won't do such a thing, you know.
00:14:11It's different from asking to have
00:14:13half a Japanese radish, you know.
00:14:14If you ask them to halve the Japanese radish they'd do it for you.
00:14:16It's okay... if it's a Japanese radish.
00:14:19What if you said just the fresh strawberry
00:14:21on the strawberry cake?
00:14:22The fresh strawberries on the cakes are sour.
00:14:29The strawberries on the cake need to be out
00:14:31in the stores before they are fully ripe,
00:14:34they are picked while they are sour,
00:14:36so it can't get sweet. But this is unrelated...
00:14:53Not by using equations or things like that
00:14:55but tell me what you have to do to get the answer.
00:14:57Buying two thousand... two... 2,100 yen exactly...
00:15:00We don't need to... it's okay if we have change left over, right?
00:15:02It's okay if there's left over.
00:15:03It's good if you have change in any case.
00:15:05Change, or else it's also okay
00:15:07if you use all of the 2,100 yen, you know.
00:15:22Well there is one minute of remaining time.
00:15:24I don't understand this.
00:15:29You're all good at this setting up an equation
00:15:31and suddenly spitting out an answer.
00:15:33Try doing it with that method.
00:15:55Okay.
00:15:58Then... we'll have midway presentations.
00:16:04Then people who think they have a way
00:16:06that seems to work...
00:16:08and understand the method
00:16:09you are paper, right?
00:16:11Not yet, now.
00:16:12People who had no idea how to do it...
00:16:14you're rock... okay?
00:16:18Okay, people who think it's best to do it this way, but say...
00:16:20You don't understand... you don't have confidence, are scissors, okay?
00:16:26Although from looking at what you were writing
00:16:27it seems like rocks are plentiful.
00:16:28But, I'll try and ask you, okay?
00:16:29Okay, then students who understood
00:16:30the way of thinking are paper.
00:16:33And then... people who say that you can do it
00:16:35to some extent and you understand it are paper, okay?
00:16:37People who say... I don't understand it at all are rock, okay?
00:16:40People who say that they are in the middle are scissors, okay? Okay.
00:16:42Then one, two, and... three.
00:16:50Oh... there are no paper people.
00:16:53What's paper?
00:16:54Paper is people who say that they understand it completely.
00:16:57One person.
00:17:01Okay.
00:17:02Then scissors people and paper people,
00:17:05there are even quite a few rock people who responded, right?
00:17:07Okay, then I will try and ask a few people, okay?
00:17:09Okay, then Hara.
00:17:11How did you think about it?
00:17:13What?
00:17:18I... didn't understand it at all but...
00:17:25First of all...
00:17:28I thought that I should calculate...
00:17:34How many of the 230-yen ones I could buy and...
00:17:38In the beginning... when I did it with 10...
00:17:43It ended up being 2,300 yen so...
00:17:47It's not good because it's over the amount so...
00:17:50And then next when I did it with nine...
00:17:55When I did it with nine...
00:17:57it was 2,070 yen and... it was okay but,
00:18:02you need to buy 10, so when I calculated it...
00:18:13Two... 2,070 plus...
00:18:18Two hundred yen is...
00:18:20With 2,270 yen and...
00:18:23You go over.
00:18:24You go over, don't you? Okay.
00:18:25So then... you keep reducing the numbers and...
00:18:28Keep reducing and... when you do it with eight on this side and two this side, then?
00:18:29When I did it-
00:18:30When you did it?
00:18:32Time ran out and...
00:18:33Time ran out and...
00:18:34I couldn't do it to the end.
00:18:35You couldn't do it to the end.
00:18:37Okay.
00:18:38Raise your hand... if you say that
00:18:40this way of thinking was really similar to yours.
00:18:43Hara started counting from 10, but...
00:18:45there may be people who started counting from this side.
00:18:48People who say that they used this way of thinking.
00:18:52Okay. Only, Ikui?
00:18:55Arai?
00:18:56Okay. Then Ikui, Arai, Joji, right?
00:18:58Then Ikui... where did you find
00:19:02an answer that was exactly even?
00:19:04Or could you not find the answer?
00:19:06Were you at the point in which you were do-
00:19:08counting it like this but time ran out?
00:19:10Did you find it in a flash?
00:19:14The 230-yen one...
00:19:18You buy three of them and...
00:19:19Three? Then how much does it become?
00:19:22Six hundred ninety yen.
00:19:23Six hundred ninety yen.
00:19:26Seven.
00:19:28Two thousand ninety yen.
00:19:29Wait a minute.
00:19:31200-yen ones how much does it become?
00:19:33One thousand four hundred yen.
00:19:34One thousand four hundred yen. Okay.
00:19:35How much is it... if you add it?
00:19:37Two thousand and seventy yen.
00:19:38Two thousand-
00:19:39Oh. Two thousand ninety yen.
00:19:40Ninety yen.
00:19:43So that means if you buy three 230-yen cakes
00:19:46and seven 200-yen cakes,
00:19:50then it becomes 2,090 yen.
00:19:51You get 10 yen in change.
00:19:53That's why you could buy three of these.
00:19:55And as for this, if you buy seven then...
00:19:57With 2,100 yen there is only 10 yen left.
00:19:59And with only 10 yen you can't buy anything, so it's this.
00:20:08I'm not done yet.
00:20:09Middle... You are still in the middle of doing it.
00:20:15What?
00:20:17I'm still doing it.
00:20:18Still doing it. As for Arai, he couldn't
00:20:21print out what was in the hard drive in his head, right?
00:20:26This... then something else...
00:20:28students who say, "I did this."
00:20:32Kamon and Luiko and who else?
00:20:35Other people.
00:20:37No one?
00:20:39What's yours, Kamon?
00:20:41How do you... work it out?
00:20:43What did you set up?
00:20:47Huh? How did you do it? Your method?
00:20:49Inequality equation.
00:20:50You set up an inequality equation. Okay, what about Luiko's?
00:20:51Inequality equation.
00:20:52You set up an inequality equation?
00:20:53Then what about other people? Isn't there anyone?
00:20:58No one?
00:21:01Then the other people can't buy them.
00:21:02You know, the cakes, counting them one-by-one
00:21:04is a really ordinary way of doing it, you know.
00:21:05Isn't there anyone else?
00:21:06Maruya's was also an inequality equation, right?
00:21:09We'll get to you later, so wait a little, okay?
00:21:10Other people.
00:21:11How did you do yours, Bancho?
00:21:13Huh?
00:21:14Yeah.
00:21:16You wrote multiply by something,
00:21:17multiply by something, right?
00:21:18How did you do that?
00:21:19The same as that.
00:21:20It's the same as this, right?
00:21:21And then who else was it now?
00:21:24Nagase's one also used a ratio, right?
00:21:26Is it the same as this?
00:21:27It's different? What is it?
00:21:28Huh?
00:21:29Inequality equation.
00:21:30Inequality equation?
00:21:31Okay.
00:21:32Then... are there others?
00:21:34Who used a completely different way of thinking?
00:21:37No?
00:21:38Then... I've thought about it, too, so...
00:21:42Do you all understand it?
00:21:44You bought... ten... 230-yen cakes.
00:21:50You're told to buy a lot and so in reality
00:21:51you want to buy all 230 yen cakes, right?
00:21:53Then how much money is needed?
00:21:54[ BB: Method of thinking. Ten 230-yen cakes. ]
00:21:55Two thousand three...
00:21:56In reality 2,300 yen is required, right?
00:22:00But you're short 200 yen.
00:22:02You are short... 200 yen.
00:22:06You're short. You thought...
00:22:09that you would buy a cake that is...
00:22:1030 yen cheaper than... the 230-yen cake.
00:22:11[ BB: Short 200 yen ]
00:22:12Buy a cake that is 30 yen cheaper and...
00:22:14You buy a cheap cake and...
00:22:15replace this needed 200 yen for a cake
00:22:16that is 30 yen cheaper, okay?
00:22:17[ BB: 30-yen cake ]
00:22:24You're short 200 yen, you know.
00:22:25But, let's buy them a cake that's not 230 yen
00:22:27but a cake... that is 30 yen cheaper.
00:22:29Then 30 yen is going to be saved.
00:22:31With each, 30 yen is going to be saved.
00:22:33How many cakes that are 30 yen cheaper do you need
00:22:35to buy in order to make up the 210 yen shortage?
00:22:39This needed part.
00:22:43How many cakes that are 30 yen cheaper do you need
00:22:45to buy to make up the 210 yen shortage?
00:22:47Can you make up the 210 yen?
00:22:48Seven.
00:22:50Yeah. If you buy six, six times three is 180 yen,
00:22:53so you are still 20 yen in the red, right?
00:22:56However... if you buy seven of these...
00:22:58you will have 210 yen left over, right? The money, right?
00:23:00[ BB: Seven ]
00:23:03That 210 yen is applied to this 200 yen, you know.
00:23:06Then if you buy seven of the cakes that are 30 yen cheaper,
00:23:11Three.
00:23:12It's three... did anyone do it like that?
00:23:14Someone who did it like this?
00:23:16There probably isn't anyone, right?
00:23:19You're short 200 yen so... let's make up for the
00:23:21missing cost with cake that is 30 yen cheaper.
00:23:23You can make up for it if you buy seven,
00:23:26so this is three. In that way.
00:23:28It was good, right? Then I'll ask you.
00:23:30Okay... Luiko.
00:23:35The total 230 yen, oh...
00:23:39It's for some amount and make that amount X and...
00:23:46You need to buy 10 of the 200-yen ones.
00:23:50So 10... make it 10 minus X and...
00:23:55And the total has some amount of two- 230-yen ones.
00:24:02And the 230-yen ones are 230 X. And...
00:24:07the 200-yen one is 200...
00:24:11bracket 10 minus X... And then... then...
00:24:19200- 230 X plus 200 bracket 10 minus X...
00:24:28is less than, minus, less than or equal to 2,100 yen.
00:24:36And you form the inequality equation.
00:24:39Okay.
00:24:40You said that this was the inequality equation, right?
00:24:43Okay.
00:24:44Did you understand the meaning?
00:24:46Perfect.
00:24:47You get it better with Luiko's explanation than with mine.
00:24:49Okay. Try and raise your hands.
00:24:50People who say that they got it with Luiko's explanation.
00:24:53One person?
00:24:54Only Maruya? Two people? Three people?
00:24:56Four people? Just four people is it? Five people? Okay.
00:25:00Then... please explain it next, Ryo.
00:25:01Please explain it in a way that is a little more understandable.
00:25:03Try and explain it in a way in which...
00:25:06a few more people will say... that they understood.
00:25:09The method of explanation is okay with this.
00:25:13Okay.
00:25:25You can't do it?
00:25:26You don't know?
00:25:32Okay. Then... I'll start talking from this point okay?
00:25:36To tell you the truth I was going to
00:25:38talk about today, what Luiko set up.
00:25:41But I wanted you to find a number...
00:25:42of ways to come up with it so...
00:25:44I did it so that I would have you think about it, right?
00:25:47Three, four, five, six. Okay.
00:25:48One, two, three, four, five, six.
00:25:50Okay.
00:25:52One, two, three, four, five, six.
00:25:54Oh, it's not five, six...
00:25:56there's five people here.
00:25:58One, two, three, four, five, six. Here.
00:26:22Okay. From there, and so...
00:26:26While talking so that everyone will say,
00:26:28"I see," while understanding Luiko's explanation,
00:26:31we are going to try and do it using that problem,
00:26:33using an inequality equation problem, okay?
00:26:35You want to buy a total of 10 cakes in which
00:26:37one is 200-yen and the other is 230 yen.
00:26:41And you want to make the total less than 2,100 yen.
00:26:44In order to buy as many 230-yen cakes as possible,
00:26:47what is the maximum that you can buy?
00:26:49That is the problem.
00:26:50And what is the thing that you want to find? Pinko?
00:26:53What do you need to answer?
00:26:55How many 230 yen cakes you buy.
00:26:58It's a problem asking how many 230 yen cakes
00:27:02So that's why you're going to think of it
00:27:04as changing the 230-yen cake into X.
00:27:07so you should think of changing the 230-yen cake into X.
00:27:09[ BB: Buy X amount of 230-yen cakes ]
00:27:14When doing that... you need to buy
00:27:1710 cakes all together. You need to buy ten.
00:27:21Right?
00:27:22Then, Qumi? If it's six of this cake, then...
00:27:26how many of this cake do you need to buy?
00:27:29Four.
00:27:30Four. How did you calculate it?
00:27:32What?
00:27:34Four.
00:27:35So how do you calculate it?
00:27:36How do you know that this is four?
00:27:39What?
00:27:40Because it's not enough.
00:27:42Yeah, so how do you calculate it?
00:27:44What's the equation here?
00:27:47Huh?
00:27:48What do you add to six to get this ten?
00:27:50Then... then how many is it here?
00:28:07X.
00:28:08What?
00:28:09That's why you're in trouble
00:28:10if you are fooled by the number here.
00:28:12If this is six then it's probably how many here, Ryusaki?
00:28:16Qumi is saying that it's four,
00:28:18but how do you get this here?
00:28:21It's four, but how do you come up with four?
00:28:27Ryusaki, how do you come up with four here?
00:28:29Subtract.
00:28:30You need to subtract, right?
00:28:31It's good if 10 minus six is four here.
00:28:33If it was seven here, then you would
00:28:36write 10 minus seven, right?
00:28:38If this were nine here then you would
00:28:40think of this as 10 minus nine.
00:28:43So if you subtract one of the numbers
00:28:44from this number, from the total number,
00:28:46then you get the remaining number.
00:28:48And the problem is,
00:28:50if you make the number on this side X,
00:28:52then what will this be if you do that?
00:28:54Here.
00:28:57Joji. What will this become?
00:29:01Here.
00:29:03You haven't been listening, have you.
00:29:05If this were three,
00:29:06then this can be found by going 10 minus three.
00:29:08If this were four, then this is 10 minus four.
00:29:11If this is five, then this is 10 minus five.
00:29:13Then if this is X, then what is this?
00:29:16Ten minus X.
00:29:17Yeah. It'll become ten minus X.
00:29:20What this is saying is that you can only buy
00:29:2210 minus X number of the 200-yen cakes.
00:29:25It will come up here.
00:29:26It's 10 altogether and if you make this X,
00:29:29then here... you need to subtract this number.
00:29:31If you subtract this number from 10
00:29:32then you'll always arrive at the number left over.
00:29:34That's why it'll be the case that
00:29:36you can buy this many 200-yen cakes.
00:29:38The amount you bought, right?
00:29:40This will be the amount here.
00:29:41If you do that, what would the cost be
00:29:43if you bought only X number of 230-yen cakes?
00:29:48If you multiply the 230-yen cakes at this price
00:29:50by X then you'll get the total cost, right?
00:29:52It's 230 X, you know.
00:29:53Because you're only going to buy 10 minus X
00:29:55of the 200-yen cakes, the cost will be this.
00:29:58Then since you only have 2,100 yen with you,
00:30:00you'll be in trouble...
00:30:01if it isn't less than this.
00:30:03And so you will get this equation, okay?
00:30:07What is the equation?
00:30:08Oh, I can't write it, can I?
00:30:10I'm wondering what the equation is so...
00:30:11The equation is 230 X plus
00:30:13200 bracket 10 minus X is less than or equal to...
00:30:15[ BB: Equation ]
00:30:18Two thousand one hundred.
00:30:22Okay, then let's try and solve this, okay?
00:30:24Okay, the 230 of this 230 X stays the same.
00:30:27Okay, Sakai,
00:30:28how much is it here when you take the parentheses off?
00:30:30Huh?
00:30:31I took the brackets off now, so here.
00:30:35Multiply this and this.
00:30:37Mm?
00:30:38How much is it when you multiply it?
00:30:49How much is it if you take off the brackets?
00:30:56Well then how do you do two bracket X plus three?
00:31:00Two X.
00:31:02Well then remove the brackets.
00:31:11I did it. I did it.
00:31:20Four plus five.
00:31:25You multiply it, right?
00:31:34Huh?
00:31:35Bracket... 200 times 10 is see...
00:31:41Two thousand.
00:31:42Oh, 2,000, right? Two thousand. Okay.
00:31:44Two thousand... minus, you multiply this so...
00:31:46this time on this side so okay.
00:31:47Two hundred X.
00:31:48Two, 200 X. Okay. Less than or equal to 2,100.
00:31:53Okay. Then which is the next one that you transpose?
00:31:55Two thousand.
00:31:56Two thousand. Okay.
00:31:57We're going to bring the plus 2,000 to the other side.
00:31:59And 230 X minus 200 X is
00:32:03less than or equal to 2,100 minus 2,000.
00:32:08The sign changes, so please be careful, okay?
00:32:09When you transpose it, okay?
00:32:10Then 30 X... 30 X is less than or equal to...
00:32:13100. Okay.
00:32:17Then you're going to divide both by 30 on both sides,
00:32:20so it becomes X is less than equal to...
00:32:23100... thirtieths but...
00:32:26I'll erase the zero here, okay? It'll become 10-
00:32:29Thirds.
00:32:30Thirds.
00:32:31What will 10 become if you write it in decimals?
00:32:36Three point three three three three three, right?
00:32:39If I asked you to find the largest integer...
00:32:42that is smaller than three point three...
00:32:45it will come out as three.
00:32:47I can't really write the answer, but okay...
00:32:48you can buy three... up to three... of the 230-yen...
00:32:51thirty yen... cakes.
00:33:00If you present it... like this... it's good.
00:33:04Things presented like this are
00:33:05solved using an inequality equation.
00:33:07[ BB: You can buy up to three of the 230-yen cakes. ]
00:33:09Which is easier, doing it one-by-one or
00:33:11using an inequality equation?
00:33:13An inequality equation.
00:33:14It's easier to use the inequality equation, isn't it?
00:33:16And so today what I would like you to do from here is,
00:33:19we already did this in the method of thinking but...
00:33:21Inequality equation.
00:33:23I would like you... to know...
00:33:26the good qualities of...
00:33:41setting up an... inequality equation,
00:33:43right... inequality equation so...
00:33:45we thought about it... with a problem like this.
00:33:47[ BB: Learning the good qualities of finding the answer by setting up an inequality equation. ]
00:33:50If you were to solve it without using an inequality equation
00:33:52you need to check it out quite a lot, one-by-one, a lot.
00:33:55Hara could solve it because it was 10,
00:33:58but what if you were to buy
00:34:00100 of these two cakes together...
00:34:04Ninety- figure out 100,
00:34:06and figure out 99, and figure out 98,
00:34:08and figure out 97, and-
00:34:10You need to figure out all of the numbers
00:34:12between one and 100, don't you?
00:34:14However, if you used a method like this that Luiko used...
00:34:18you will arrive at the answer quickly.
00:34:20Therefore, you don't need to figure out each number one-by-one.
00:34:22So working it out by making...
00:34:25an inequality equation has a lot more...
00:34:28good qualities... than counting it one-by-one.
00:34:30That's what it's about, all right?
00:34:32So then and so...
00:34:33if there are good qualities like that then...
00:34:36we're saying that.
00:34:38So there are two problems on the right side.
00:34:43If you count it one-by-one
00:34:45you will be in an incredibly terrible situation.
00:34:47As we just did in the cake situation,
00:34:50set up an inequality equation by yourself and
00:34:52find out up to how many apples you can buy.
00:34:54Or if you're doing the problem at the bottom,
00:34:56try to solve the problem about
00:34:57how many pears you can buy by setting up an inequality equation.
00:34:59Work it out and find an answer.
00:35:02Because finding the answers one-by-one is hard-
00:35:04I wonder if you see the numerous good points
00:35:05of setting up inequality equations,
00:35:07and, well, that you'll set up
00:35:09inequality equations yourself and
00:35:11try to find the solutions.
00:35:13That's what it's all about, okay?
00:35:14Is it okay?
00:35:16Okay. Then and so...
00:35:18people who haven't written this here,
00:35:20write it, and then do problem one.
00:35:23Try to set up an inequality equation
00:35:25by yourself in the same way and
00:35:27try to solve the problem.
00:35:41This is... the total so...
00:35:43you don't have it... see?
00:35:47This is attached.
00:36:01It's faster than counting, right?
00:36:12It's okay. Now, work out the problem.
00:36:14This expresses this in the same way as this.
00:36:17Oh, solve this on the top.
00:36:28That's good.
00:37:14It's like this, you know.
00:37:16Twelve times.
00:37:18Not 12, it's 70 times 20, you know.
00:37:21This is 20, isn't it?
00:37:23It's a bracket so, okay?
00:37:24It's not a 12, you know.
00:37:26I got it. Twenty.
00:37:30numbers that you wrote, could you?
00:37:47It's okay, Tanizaki, here.
00:37:50Try this and work it out like this.
00:37:58Sakai's one is also good, isn't it?
00:38:00Okay, you've got it.
00:38:06Then now it's easy, right?
00:38:08It's easy, right?
00:38:11This isn't X here, but...
00:38:13you're going to buy 20 in all, right?
00:38:16So here you will get the number you subtracted...
00:38:18from the total amount of 20.
00:38:24And so 20 minus... negative X.
00:38:29And so the price here...
00:38:31you multiply the price of one of them, and
00:38:34this amount, so this becomes 120 X. Okay?
00:38:41It becomes 70 parentheses.
00:38:45You can't write it... if it's like that.
00:38:46Please write the 70 sort of more on the side.
00:38:53Twenty minus X.
00:38:55Okay. Now you've got it.
00:38:56And then put these together and
00:38:58make this smaller than four.
00:39:00Huh? Two hundred.
00:39:06Just a moment. It's all right now, right?
00:39:11Oh, Ueda, that's good. Okay, it's done.
00:39:16Oh, Ueda, yours is good, too.
00:39:17You've arrived at the answer, right? Okay.
00:39:18Where'd it go, Waka?
00:39:24This is okay, you know?
00:39:27This is... 120 X plus,
00:39:30how much is this if you multiply it by this?
00:39:33Two times seven, 14, right?
00:39:36One thousand four hundred seventy two thousand.
00:39:42This is four. Then you have to transpose it.
00:39:44There is seven, 700.
00:39:46Twent- this is 70 times 20, so next is four, right?
00:39:52Okay.
00:40:46[ BB: 120-yen apples ]
00:40:55[ BB: 70-yen tangerines ]
00:40:56[ BB: Total ]
00:41:57Okay, I guess I'll have you write it.
00:42:07Are you done?
00:42:09Did you do it?
00:42:10Then work it out there... will you?
00:42:14This should be fine, right?
00:42:17[ BB: Buying Twenty. One hundred twenty-yen apples. Seventy-yen tangerines. Total. ]
00:42:18Could you write it?
00:42:20Isn't it good? It's good.
00:42:22Divide, you can divide it.
00:42:29Then... Bancho.
00:42:31Look at the figure and set up an equation
00:42:33and work it out, okay?
00:42:34What number?
00:42:35Number two.
00:42:37Number two?
00:42:38Yeah.
00:42:50Write it without looking at anything, okay?
00:42:52Because I wrote-wrote that you would buy 15.
00:43:02Mm, I just saw someone's eyes.
00:43:03Okay, Watabe.
00:43:04Uh, wait a second.
00:43:05Watabe, please write number one, okay?
00:43:09You don't understand if you don't look at anything.
00:43:10It's not written.
00:43:12This is going to appear in the equation.
00:43:14Oh, how much is it for the baskets?
00:43:15Oh yeah, I didn't write the basket prices. Sorry.
00:43:19Eighty yen, isn't it?
00:43:20Eighty yen.
00:43:38The total... was 1,000 yen, wasn't it?
00:43:40Hm? Oh. I should write the totals, too, shouldn't I? The total, sorry.
00:43:43Less than 1,000 yen.
00:43:45Watabe's is less than 2,000 yen.
00:43:46Two thousand?
00:43:48Please write 2,000 yen here. Oh, okay.
00:43:56Try hard and work it out.
00:44:03Just one more step, just the answer.
00:44:05Oh, you need to display the answer.
00:44:11Eight?
00:44:14It's wrong?
00:44:15What?
00:44:16What is this?
00:44:17What?
00:44:19of this inequality equation is wrong, isn't it?
00:44:21Isn't it okay? Because... this is 10, right?
00:44:30With 80?
00:44:32It's this value here.
00:44:33Two times nine?
00:44:35Seven hundred fifty.
00:44:37Aren't you missing the 50 here?
00:44:45Oh... the response is okay with this.
00:44:48The answer is not this though, is it?
00:44:54Huh?
00:44:57Is it this?
00:44:58This is good.
00:45:00This is the answer to the inequality equation.
00:45:02But, the answer to the problem has to be this, right?
00:45:10When asked to work out this inequality problem,
00:45:12this is- This has to be the answer here, right?
00:45:14However, this won't be the answer to the applied problem so-
00:45:16One hundred seventy over 20.
00:45:19Seventeen over two, right?
00:45:22So teacher, if you do it like this, is it correct?
00:45:33That should be that way, right? Okay.
00:45:38Ueda, how far did you go?
00:45:44Fifty times 15 is look...
00:45:46Not yet?
00:45:49It's 75, you know. Then it becomes 750.
00:45:54For example, how do we write the answer?
00:45:56What are you going to write?
00:46:00What? Pears, right?
00:46:02Up to how many pears can you buy?
00:46:09It's 70 times 20, so it's not 140,
00:46:12but it's only one zero, right?
00:46:41There the six is... 60... you're missing one zero, aren't you?
00:47:14Please look at number one first. If you say that you will buy only X 120-yen apples then...
00:47:20You're going to buy a total of 20.
00:47:22So, as for the tangerines, you need to buy only the total 20 minus X tangerines.
00:47:26And the price of the apples is 120 X.
00:47:29And the price of the tangerines is 70 parentheses 20 minus X.
00:47:32And the total that you have is 2,000 yen, you know.
00:47:35So you're asked to make it less than 2,000 yen so...
00:47:37One hundred twenty X plus 70, parentheses 20, minus X, is less than or equal to 2,000.
00:47:42And if you try to find the answer you get X is less than or equal to 12.
00:47:47That's why you can buy up to 12 apples.
00:47:50We're going to try to see if this is true or not, okay?
00:47:58Then what is the cost?
00:48:01Is there anyone who knows what is 12 times 12?
00:48:03Didn't I teach this to you before?
00:48:04One hundred forty four.
00:48:05It's 144, right? Okay. One thousand four hundred forty yen. This is the price of the apples.
00:48:09Then, you need to buy eight of the 70-yen tangerines so seven times eight, 56.
00:48:14And all together it's exactly 2,000 yen.
00:48:20About it being exactly 2,000 yen, why did it become exactly 2,000 yen here?
00:48:23Since it's divisible.
00:48:24Because here we got 12, a number that was divisible, right?
00:48:26Right. We got it because the 12 could be divided perfectly into it here, right?
00:48:28That's why it ended up being exactly 2,000 yen.
00:48:30However, this side. Okay.
00:48:32You find it in the same way. The pears are X and you're going to buy 15, so the persimmons are 15 minus X.
00:48:37The price of the pears and the price of the persimmons... and even the basket will be included as well this time, right?
00:48:42It's asking you to limit it to 1,000 yen all together. So, if you set up an inequality equation you get this kind of equation.
00:48:46Seventy X plus 50, parentheses 15, minus X, plus 80, is less than or equal to 1,000. Please work this out.
00:48:56This is the answer of the inequality equation, okay?
00:48:59You need to present this, okay?
00:49:00Instead of just suddenly writing the answer eight- if you first work this out...
00:49:04You get an answer of 17 halves, okay?
00:49:07You need to find this first. Now you need to pinpoint it like this.
00:49:14Then... if you buy eight 70-yen pears, then seven times eight equals 560 yen.
00:49:19If you do that, then how many 50-yen persimmons do you buy?
00:49:23You buy seven? Then seven times five equals 350 yen. All together... 910 yen.
00:49:32Then... you'll have 90 yen in change coming back.
00:49:34What?
00:49:36Oh, there's the price of the basket.
00:49:37The basket price is 80 yen so...
00:49:40It's altogether 990 yen, and you'll only get 10 yen in change. That's what it's about.
00:49:45What we talked about today was... the answer from inequality equations... that is...
00:49:50When solving problems it's often easier to set up an inequality equation and find the answer,
00:49:54than count things one-by-one and find the number.
00:50:01That's why although it may be tedious... for the applied problems of inequality equations, okay?
00:50:05Instead of looking for the answer one-by-one you find it by changing the parts written in Japanese to mathematical terms and solving it.
00:50:15Because an inequality equation has a good quality like this. This is what we talked about.
00:50:20Is it okay?
00:50:22Is it okay?
00:50:23Yes, okay.
00:50:25Then I'll pass out the problems and finish off. What number should I pass out, today?
00:50:29Is it number nine?
00:50:32It's number nine. Number 10.
00:50:33Then I'll hand out the problems for number 10 and finish.
00:50:36From what number to what number are there?
00:50:38It ends with 10.
00:50:39Inequality equations end with this.
00:50:46One, two, okay.
00:50:54Four more.
00:50:55Four more? Okay.
00:50:56One, two, three, four, okay.
00:50:59One, two, three, four, five, okay.
00:51:02One, two, three, four, five, six, okay.
00:51:07Okay.
00:51:09Okay. Then we'll say our greetings and finish off.
00:51:12Student officer. Lead with strong voices since we're finished.