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00:00:00The thing that we need is and see that you remember.
00:00:58The thing that we need is and see that you don't have to do it.
00:00:59number one qst bar
00:01:02dub and dutch grammar question mark to write drag
00:01:05dub and dutch
00:01:06unmoor dairy creamer for a perfect cup of tea
00:01:08shalimar shame
00:01:09kuru musla
00:01:09gibboni raashul shahad
00:01:28and students you know that today our subject is mathematics and the topic we are going
00:01:33to discuss on is an equation before we start our class let me introduce mrs taputiroi
00:01:40council appointed teacher of james academy international school
00:01:43and a very warm welcome madam and the students were on the other side of the television if
00:01:49you have any kind of queries doubts and questions related to today's topics feel free to call
00:01:55the number is being displayed on the television screen now madam it has often been observed
00:02:00that students sort of opinion that mathematics is a very difficult subject to deal with and
00:02:06uh a sense of anxiety is there among the students when they face mathematical problem
00:02:11i would rather say madam and i think you will agree with me that once you accept the challenge of
00:02:16uh solving a mathematical problem and you succeed in doing so it gives you an
00:02:21uh a sense of satisfaction joy and happiness that can well be compared with winning of an oscar
00:02:30very well said i must say that is the joy of mathematics actually it is a very easy subject
00:02:37the only little thing that we need is to go on drilling if your concepts are clear it's right from
00:02:45the beginning if you pay attention you do all your drilling of the sums revise and keep your formulas
00:02:52in place and see that you remember the different methods that you're teaching then i think mathematics is
00:02:59easy because you don't have too much of um memory work it's more of working on it and the joy
00:03:06of
00:03:06getting a sum correct is really excellent and i think if you start yes it is and if you start
00:03:14really working right from the beginning you'll find that it is really simple because mathematics
00:03:20solving a sum i would say there is not only one method of doing the sum there are many ways
00:03:27so we will
00:03:28the teachers will check or anyone checking it's only seeing whether logically the steps are correct
00:03:34so what one teacher has taught or another teacher or one friend has showed you doesn't matter you can
00:03:40approach in any way you want to do your mathematics so there's no hard and fast rule that you have
00:03:45to do
00:03:45by this method so i think mathematics is an enjoyable subject and that is a subject which you can do
00:03:52at any
00:03:52time of the day very true and i can see you have already written today's topic that is the equation
00:03:58in one
00:03:59variable right proceed now we are going to do today our topic is linear in equation in one variable
00:04:08now one variable you have done equation in one variable so today we are doing in equation
00:04:14before we go on to the topic what we i want to say you have done linear inequality or we
00:04:22can say
00:04:22inequality in your lower classes also like when you were in a very small class junior classes you learn
00:04:30the numbers like if i say 20 is greater than say 52 so these are things which you have done
00:04:40or 15
00:04:42is less than 5 this is also inequality that means greater smaller so you've learned this now next week
00:04:51say in geometry we have a topic in class 9 those who are in 10 must have learned it that
00:04:59is inequality
00:05:00in geometry triangles of those who are in 9 will be doing it so we have in arithmetic we have
00:05:07in geometry
00:05:08what we are doing today is inequality in algebra
00:05:17so before we go on let us see what is this inequality the slide
00:05:26we are taking a balance now you can see a balance there you know what a measuring balance is
00:05:35so you can see there we have weights on the two pans in one pan that is in pan a
00:05:43we can see
00:05:44there is a basket of carrots and two one kg weight and in the other we have
00:05:53one two three four five six six one kg weight but what do we see the
00:06:00pointer pointer in the uh span we find that it is fully in the middle what does it show there
00:06:08is equal
00:06:08weight on both the sides if it is equal weight on both the sides that means it is an equal
00:06:17to the two weights
00:06:20weights of basket
00:06:24of carrots
00:06:28plus
00:06:30the one plus one that is the two weights that we have got
00:06:34equal to
00:06:36what have we got in the other side one plus one plus one plus one plus one plus one plus
00:06:42one
00:06:43so there are so we have the basket of
00:06:50carrots
00:06:52plus two kg weight that means there is some weight of the basket is equal to six
00:07:00so they are balanced now let us see the next slide
00:07:07can you come to the next slide please please carry on
00:07:10yes next slide now what do we see here we see there is the basket yes there are the carrots
00:07:18basket of carrots that is a one kg here right one kg but what do we see on the right
00:07:24hand side
00:07:24right hand side we can see there are basket of
00:07:31carrots
00:07:33plus
00:07:35one plus one plus one plus one plus one plus one plus one so we have got the basket of
00:07:42carrots
00:07:47two plus two is equal to four kg weight so that means now but the balance there is a difference
00:07:55in the balance what is the difference we find that the
00:08:00pan which carries the basket of carrots is lower down and the other one has gone higher up that means
00:08:06they are not equal so the two of these are not equal so what do we say here there is
00:08:14something
00:08:14different we say less than and here comes the basic question the difference between
00:08:20equation and in equation so we are coming to that soon with this with this only i'll explain so here
00:08:28i
00:08:29wrote equal to so this is not equal to why because we have seen in the pan there is a
00:08:34they are not in the
00:08:35same balance that means the pointer showed that they are different so basket of carrots plus two
00:08:43is less than four rather sorry not less than i think the pan was the right hand side was
00:08:50so this is greater than greater than right because this was we found that the can when we had the
00:08:59pan here
00:09:01this was when it was equal to and when we had this we had it like this
00:09:07so that means it's been this side so therefore this is lesser than this so therefore we say this is
00:09:15greater than this so therefore we get now suppose i take the basket of carrots that is
00:09:34now let us take the basket of carrots as equal to x kg right and what did we have there
00:09:42plus
00:09:422 and what was it equal to 6 in the second case we found that x plus 2 was there
00:09:53but it was not less
00:09:55than but it was greater than not 6 we had greater than 4 we had a weight of 4 right
00:10:04now what did we have
00:10:06here that means this is equal to look at the symbol this is greater than greater than so they cannot
00:10:12be
00:10:12both the same so this is called what sir was asking this is an equation
00:10:19and this is an in equation right ma'am uh before you proceed uh i beg your pardon ma'am
00:10:27there is a
00:10:28student named orgujit and he has some questions so may i take the phone call yes please carry on
00:10:34yes ma'am my question is uh six difference between equation and union equation once more
00:10:43yes dear i will be discussing a lot about equation and in equation i'm coming to it we have just
00:10:50shown
00:10:50with the diagram and we'll come to equation i'll always refer to the equation why because you'll have
00:10:57done already equation from class 6 you are doing equation or rather in class 5 also a little bit
00:11:03mainly in class 6 you have done equation so the relationship i'm bringing with it so in this just
00:11:10carry on watching now here what do we have is it okay yeah so here we have x plus 2
00:11:18equals to 6 so we are
00:11:20equating them so this is an equation and here x plus 2 the two balance they are not equal and
00:11:29this was
00:11:29more than this so we wrote greater than 4 this is an in equation now let us see what happens
00:11:36let us go on to
00:11:38this x plus 2 equals to 6 now when is this true the only thing you can find out the
00:11:46missing number
00:11:47we can solve it we can solve it out if x i put equal to 4 what do i get
00:11:534 plus 2 is equal to 6
00:11:57so from this what do you get that the basket of carrots is a weight 4 kg right so we
00:12:07have got with
00:12:07the equation we found that it is true that means it's true for only one value now let us see
00:12:14this
00:12:15x plus x plus 2 greater than 4 now suppose i take x equals to uh 1 suppose my weight
00:12:26of x is
00:12:271 so 1 plus 2 is that greater than 4 no 1 plus 2 is equal to 3 and it
00:12:34is not greater than 4 so x cannot
00:12:36be 1 kg now let us see if i put x equals to 3 now what do we have 3
00:12:45plus 2 equal to 5 is 5 greater than 4
00:12:50yes it's true so x can take the value the basket of carrot might be 3 kg also so because
00:12:59it's satisfied if i take
00:13:00x equals to x equals to say 4 4 4 plus 2 that's equal to 6 6 so is 6
00:13:09greater than 4 yes yes 6 is greater than 4
00:13:13now what do we see actually here in equation we found that this really equal equal to sign is valid
00:13:23for only
00:13:24one value of x but here we find that this is true for more than one value so therefore we
00:13:37see
00:13:37that equation has is true for only one value but in equation is true for
00:13:46is true for is true for more than one value it may be one value it may be more than
00:13:52one value also
00:13:55now let us go to our properties i hope all is this much is clear of the concept of your
00:14:06equation and
00:14:08in equation in equation now we are going to deal with
00:14:24properties properties
00:14:30properties of
00:14:35inequality inequality that is what is not equal
00:14:43now we are going to do properties of inequality so what do we get here we find that suppose i
00:14:51take a
00:14:52number we have a general proof
00:14:56next slide um we are going on to say i'm taking a number nine greater than six this is true
00:15:06right
00:15:07okay now if i add three add three to both the sides of the equation what do i get
00:15:18nine plus three here i'm also adding six plus three what is my answer here
00:15:25twelve what is my answer here nine is 12 greater than nine
00:15:30true yes so 12 is greater than nine so we started with nine greater than six but by just
00:15:39adding three it hasn't changed the inequality sign it still remains the same let us see subtraction
00:15:52it's nine again nine greater than six i'm subtracting nine minus three and here six minus three
00:16:00what is nine minus three that is six what is six minus three three so is six greater than three
00:16:08yes
00:16:09yes so six is still greater than three so therefore again the equality remains the same by subtracting a number
00:16:17so we can say by adding or subtracting any number
00:16:23to a inequality it does not change the inequality it still remains greater than
00:16:30oh now let us see so i hope it is clear we can add or subtract any number on any
00:16:40side of both the side of the inequality
00:16:42both lhs and rhs yes
00:16:53discomfort with this now let us see with multiplication
00:16:59multiplication first multiplication and division let us see multiplication and
00:17:09addition and subtraction uh have already been done yes and now multiplication and division right now
00:17:18now let us think of this number that is um nine greater than six i'm doing my division first okay
00:17:29nine divided by
00:17:34three
00:17:35three and six divided by three what is this this is divided by three yes six divided by three
00:17:46now nine divided by three that is three six divided by three that is two so is three greater than
00:17:55two
00:17:55yes yes so still with multiplication also there is no change the division also no change again i'm doing
00:18:04multiplication also nine into three six into three
00:18:1127 and this is 18 so it's 27 greater than 18 so that is true so again it is true
00:18:19that means
00:18:20whether addition subtraction or multiplication or division by a num positive number number we find that the
00:18:30operation remains the same and for addition subtraction we can use any number positive or negative here i'm taking only
00:18:38positive number now suppose i
00:18:40okay
00:18:45now this you have to watch very carefully
00:18:50division
00:18:51now again i'm starting with nine greater than
00:18:55six now i'm dividing by
00:19:00both sides
00:19:03five
00:19:04five minus three
00:19:07so i'm doing nine divided by
00:19:10minus three six divided by
00:19:13minus three
00:19:16now what do we get this becomes minus three and this becomes minus two
00:19:24two
00:19:25have a look now before we go on to this let us have a look at this
00:19:32i'll come to this later also now you are familiar with
00:19:37i hope you can see it
00:19:42so we have got a axis here now this is a line that is a real number line
00:19:48this is zero one two three four five
00:19:53now what do you see here one two three four that means on the right hand side
00:19:57the numbers are going on increasing
00:20:00and on the left hand side
00:20:02minus one minus two minus three minus four
00:20:05that means our positive numbers are on the right hand side and our negative numbers on the left hand side
00:20:11positive side they go on increasing negative
00:20:15side they go on decreasing that means from this what can we say
00:20:19that minus three is lesser than minus two so here what are we having
00:20:27minus three is less than two minus two so what is the change here
00:20:33this was greater now this has become less so when we divide by a negative number
00:20:41the inequality changes
00:20:46now let us go again
00:20:49nine greater than six multiplying by minus three and six also by minus three what do i see here
00:21:00minus twenty seven minus eighty now can you tell me i can't show with my small ruler all the numbers
00:21:10so according to this which is your greater number
00:21:16so here see minus three is greater than minus four so if you see here
00:21:24what about minus eighteen and minus twenty seven so minus eighteen is greater than minus twenty seven
00:21:31so we have a lesser sign here
00:21:36once more i need to interrupt you uh sorry ma'am another student is there on the phone line
00:21:40let me take his question akshay prakapsing is there yes akshay please go on
00:21:46uh sir i have a question that uh is it necessary to draw a number line
00:21:53can you repeat your question please yes i think i have understood you have understood okay
00:21:59here we we are just explaining the properties of addition subtraction multiplication
00:22:05of numbers that is addition subtraction multiplication with positive numbers negative numbers what it
00:22:13comes because these we are going to use them in in equation unless these concepts are clear you won't be
00:22:19able to solve them out here we don't represent the number line we have seen that many students make a
00:22:26mistake of understanding which side are the positive numbers and which side are the negative numbers
00:22:31so what they do is they mark here all the positive and here all the negative and they cannot understand
00:22:37which is bigger and which is smaller so you must understand that the numbers in case of negative number
00:22:45this number 27 in a positive number would have been greater than this number
00:22:52in a positive number so 27 would have been greater than 18 but we find according to this that's why
00:23:00i'm
00:23:00showing you don't have to draw the number line this is to show how it is placed on the number
00:23:06line
00:23:06which side is the greater number which side is the smaller number so from here you can conclude
00:23:13that minus 27 is less than minus 18 right i hope you have understood yes sir so we have done
00:23:23all the
00:23:24properties which we are going to use in our in equation may i take another phone call ma'am yes
00:23:34sure if you have
00:23:35permission uh joy marlo rana is there on the phone line uh yes joy marlo i want to ask hello
00:23:44ma'am yes i want to
00:23:46ask that um in in linear equation yes what question please please place your question please
00:23:57i'm i'm asking that in the in the in the equation can we use or this is that
00:24:04linear equation can we use or implies that uh such kind of question is there implies that means when you
00:24:12are solving it see when i'm solving it i'll be showing all the method of how to solve the equation
00:24:19so don't worry about that we will come you see the whole thing and you'll find out that all your
00:24:24doubts
00:24:24will be cleared i i i i want to make an announcement ma'am uh to for the students whoever
00:24:30is uh calling
00:24:32and uh making a placing your questions here please make sure your television set is on mute mode
00:24:37until you put your television set on mute mode your question will not be audible to ma'am and your
00:24:44question will remain unanswered please uh take care of this please carry on ma'am
00:25:02now let us go on to this suppose we say three times a number is equal to 15 so 3x
00:25:14is equal to 15 that is what we interpret three times a number is equal to 15 so therefore we
00:25:23say
00:25:23this is our equation just now i've explained it's a two expressions with a equal to sign so again we
00:25:31are saying what is an equation equation is a mathematical statement where two algebraic expressions
00:25:40are connected by an equal to sign so 3x equal to 15 now this is true for what 3 into
00:25:495 that is equal to 15
00:25:53so therefore the value of x here is 5 can any other number satisfy this no there's only one value
00:26:01which
00:26:02which can satisfy that 3 times a number which can satisfy that 3 times a number is equal to 15
00:26:06now if i say
00:26:083 times a number is
00:26:13greater than 15
00:26:18so we can use 3x greater than 15 i can take example 3x less than 15
00:26:25or we can say 3x or we can say 3x 3x greater equal to 15 all these are inequality signs
00:26:34so we have got our
00:26:35in equation so 3x is greater than 15 now if i divide by we have learned the properties just now
00:26:42dividing by
00:26:433 it does not change the inequality sign so dividing by 3 on both the sides
00:26:53what do we get x is greater than 5 same thing here x is less than 5 same way dividing
00:27:03we get this all the
00:27:05same so here greater than 5 so now x greater than 5 there are so many numbers possible there's no
00:27:12one
00:27:13single solution so this is what we are getting that in equation we are getting only one solution
00:27:19in inequality or in equation we are getting more than one or one solution so therefore we are going
00:27:28on for solving equation now we will go on to a word problem your inequality and in equation their
00:27:38application in mathematics you are making us understand now students do also have question
00:27:43why do we observe inequality in our uh daily life also right right very good question so where do we
00:27:49look in inequality in our daily life now suppose if i say if in india the a person is eligible
00:27:59for
00:28:02voting only if his age of his or her age is more than 18 or equal to 18 so see
00:28:12this is fully an equation
00:28:14what are we saying x is the age and what is the condition given for you to be able to
00:28:21vote your age has to
00:28:22be greater or equal to you if you are 18 you are eligible to voting or if you are more
00:28:31than 18 also you are
00:28:32so if a person goes to vote what is to be checked the age age is what x so we
00:28:41are checking x if a person comes
00:28:44and says my age is 17 eligible no because it doesn't satisfy the inequality here so if a person comes
00:28:55and
00:28:56say i'm 25 yes eligible so this is also an equation we see it all around us say the speed
00:29:04limit of a two
00:29:06wheeler in kolkata is 40 kilometers per hour so speed limit read the word is 40 kilometer so that means
00:29:14the speed has to be it should be what less equal to 40
00:29:24maximum you can put your speed as 40 kilometers per hour so you have to keep in mind that the
00:29:32limit is
00:29:33maximum 40 you have to be within a range 40 or below 40 again an equation so you can see
00:29:41all around you
00:29:42in equation it's not that just a sum on the board or on your copy okay ma'am we have
00:29:48another student
00:29:49anunna kanojiya on the phone line and she has some questions yes anunna hello yes please go on
00:29:59do we have to drop number line in each and every question okay ma'am i i i i i
00:30:06will take the
00:30:06i will take the answer of anunna's question before that it's time for a short break we will come back
00:30:11in no
00:30:19time
00:30:23class 12 where
00:30:25Can't be due from chapter-wise question index.
00:30:30Rao Martinez.
00:30:32Vigitra Shohaika series.
00:31:19Vigitra Shohaika series.
00:31:52Vigitra Shohaika series.
00:31:55Vigitra Shohaika series.
00:32:24Vigitra Shohaika series.
00:33:24Vigitra Shohaika series.
00:33:36Vigitra Shohaika series.
00:33:53Vigitra Shohaika series.
00:34:18Vigitra Shohaika series.
00:34:50Vigitra Shohaika series.
00:35:20Vigitra Shohaika series.
00:35:21Vigitra Shohaika series.
00:35:46Vigitra Shohaika series.
00:35:49Vigitra Shohaika series.
00:36:11Vigitra Shohaika series.
00:36:19Vigitra Shohaika series.
00:36:26Vigitra Shohaika series.
00:36:39Vigitra Shohaika series.
00:36:41Vigitra Shohaika series.
00:36:43Vigitra Shohaika series.
00:36:44Vigitra Shohaika series.
00:36:46Vigitra Shohaika series.
00:36:47Vigitra Shohaika series.
00:36:48Vigitra Shohaika series.
00:36:50Vigitra Shohaika series.
00:36:52Vigitra Shohaika series.
00:36:54Vigitra Shohaika series.
00:37:05Vigitra Shohaika series.
00:37:08so we get 2x plus 3 less than 9 now 2x we do we are actually doing the same operation
00:37:18what
00:37:19we subtract isn't it i'm doing it here always minus 3 less than 9 minus 3 the inequation
00:37:27one is zero one is one one is two all these numbers are less than three so sanjay may have
00:37:36scored zero goals or one goal or two goals so there are three possibilities we have got for
00:37:44this condition that is given now someone may ask less than three we have got minus one minus two
00:37:51why not those but can we get negative score in a football match the goals cannot be negative
00:37:59so therefore we can have only possible outcomes are zero one and two so again we have solved the
00:38:09inequation here now we will actually go on to solving linear inequation ma'am you have very vividly
00:38:17described the equation and inequation and there are also questions among the questions one question
00:38:24is that what is the difference in the solution of a of an equation and an inequation yes you will
00:38:29see
00:38:29that i've discussed this question it's a good question many a time i'm going on referring when
00:38:34we are solving an equation we find the major thing we find that an equation that has an with one
00:38:41variable
00:38:41there is only one solution one unique solution you cannot have more than one solution here we may
00:38:48have one or more than one solution so solving out we have seen so this is a major difference between
00:38:55equation and inequation but the method of solving is same right we do the same operations and we carry on
00:39:02so now we are going to actually want to solving any equations may i take another phone call yes
00:39:09shafnodeep is there with his phone with his question on the phone call yes shafnodeep what do you have to
00:39:15ask
00:39:15ma'am i have a question that is section two if we attempt five out of seven questions will the
00:39:22first four
00:39:23questions be taken into account when max will be given all the best four questions which i have answered
00:39:29will be taken into account child this is not a part of the topic we are doing but even then
00:39:34i'll tell
00:39:35you the best thing to do is to answer what the options are given so there are four questions to
00:39:42be
00:39:42done from the section b that means your choice section it's better you stick to that and give time
00:39:48to recheck otherwise there are chances of going wrong with your what work you have already done
00:39:54to hurry up and do an extra sum so i think you stick to your number of choices that you
00:40:00are
00:40:01given in the question i hope that is clear so don't be in a haste always cool calm and composed
00:40:09while solving a mathematical problem
00:40:18so now ma'am you are going on to solve the in equation okay 3x plus 5
00:40:34can we have the slide solve 3x plus 5 greater than equals to 5x minus 3 can we have the
00:40:41slide please
00:40:41on the screen television screen 3x plus 5 greater than equals to 5x minus 3 represent the solution on
00:40:51the number line if yes read the question carefully yes ma'am 3x plus 5 greater than equals to 5x
00:40:58minus 3
00:40:59that is okay i've written the question down right it's not there on the slide uh i hope you can
00:41:04see
00:41:04here here 3x plus 5 is greater equal to 5x minus 3 i put it there in the slide but
00:41:10i'm explaining the
00:41:11whole thing this is the first part of your solving the in equation now greater equal to now we are
00:41:18going
00:41:18to follow the steps the properties we have done so 3x plus 5
00:41:283x plus 5 i want to first get rid of my minus 5 i'm doing here same thing i'm doing
00:41:37on the other side
00:41:39once you are familiar with their working you can avoid this step and do that mentally so minus 5
00:41:46so i could have already said that addition and subtraction subtraction do not change the
00:41:51property of inequality yes right very good so then inequality does not change so we have subtracted
00:41:58so mentally after you are used to and you have got the properties clear you can do straightforward
00:42:03that means this you are mentally thinking that this has become minus the moment you are putting
00:42:07minus so now we get 3x is greater equal to 5x minus 8 now i've got x term here i've
00:42:18got x term here
00:42:19i have to solve for x so now what will i do 3x same thing 5x minus 5x minus 8
00:42:30that means i'm subtracting
00:42:32minus 5x that is i'm subtracting 5x from both the sides so again here also minus 5x so we get
00:42:39here
00:42:39minus 2x is greater equal to minus 8 so we have added we have subtracted here we have subtracted here
00:42:49now i've come to a minus 2x so minus 2x greater equal to i have to find x so i
00:42:54shouldn't have any coefficient
00:42:56here what do i do divide by minus here what do i do divide by minus now don't forget what
00:43:00we discussed
00:43:01minus 2 when we are dividing by minus 2 minus 8 divided by minus 2 i hope you remember dividing
00:43:10by a minus
00:43:11negative number the inequality changes so we get here not greater equal to less equal to so you can write
00:43:21x is less equal to minus 4 this is a very important point to remember many students go wrong in
00:43:34this
00:43:34particular one they go on like equation when if this was an equation say minus 2x is equal to minus
00:43:428
00:43:42here it doesn't matter x would be you could have written it upon minus 2
00:43:52so we could have written it as minus 2 so therefore what this is the difference in the
00:43:58equation and in equation solving that is dividing by minus 2 the inequality changes minus and minus here
00:44:05it becomes plus and minus 2 and minus 2 cancels and we get x x is less equal to 4
00:44:11now we have to find out the solution now i'm going to do the solving before that i want to
00:44:18discuss
00:44:19a bit about your number system because i have to find the solution what will be the solution
00:44:25let us go on to the number system the slide please yes we will come to the slide shortly please
00:44:34you
00:44:35request ma'am now for our number system yes you can see in the slide also for the number system
00:44:43we have what are the different number system we have the natural numbers n stands for the natural numbers
00:44:50then we have w the whole numbers then we have the integer z or i any one of the symbols
00:44:58we may use
00:44:59then we have rational numbers you can say rational which can be expressed as a fraction rational numbers
00:45:11both positive and negative and irrational numbers
00:45:21now this is your one two three and so on all with a set of elements which are one this
00:45:28is what zero one make clear about these number system you have been doing number system in lower classes also
00:45:38but you are when come to solving an equation many go wrong with the numbers
00:45:44so integers so integers are you can have zero one two three and carries on here we can have minus
00:45:51one minus two and so on carries on
00:45:58now rational numbers are what we cannot list so many rational numbers
00:46:02before going to rational number may i take another phone call madam yes yes
00:46:06nishant singh is there on the phone line yes nishant
00:46:11hello yes nishant what yes what's your question
00:46:16actually i had a question suppose uh suppose we have an equation like this uh
00:46:23okay this equation 2x minus 3 yes greater than equal to x plus 1 minus x divided by 3
00:46:31greater than equal to 2x by 5 sir but like we can split the equation into the equation or we
00:46:37can do it separately
00:46:38so which is better to do it and how will we do it sir
00:46:41we are coming to it we will come to those type of sums also
00:46:45with the two inequality so we go step wise everything is step wise right
00:46:49so first type is this where we have one inequality sign and if you have the other with the two
00:46:56inequality i'll come in the next example
00:46:57we'll just finish discussing this and then we are going on to the next one
00:47:01please go so irrational numbers
00:47:03rational numbers any number which can be expressed as p by q
00:47:07and q are integers and q not equal to 0
00:47:11and numbers like root 2
00:47:13which cannot be expressed as a fraction etc
00:47:17they are an irrational number
00:47:19this as a whole
00:47:21is a set of real numbers
00:47:24all these number system together form the set of real numbers
00:47:28so i hope this is clear
00:47:29so let us go on to
00:47:33representing on the number line
00:47:43now
00:47:44we are taking different cases
00:47:46number 1
00:47:47suppose i said
00:47:50x
00:47:52x belongs to
00:47:55these are called replacement set
00:47:56you can just have a set of elements as the replacement set
00:47:59or you can have natural numbers
00:48:01whole numbers integers
00:48:02that means from where i will be getting my solution
00:48:05if i write x less equal to 4
00:48:07i don't know what to write
00:48:08because it is not clear
00:48:10what the numbers are
00:48:13so
00:48:18x belongs to n
00:48:20now let us draw the number line
00:48:23so
00:48:25again that number line i have shown
00:48:27so we have a straight line
00:48:30i said natural number
00:48:32the first thing
00:48:33what you have to do is
00:48:35part 1
00:48:36my solution is
00:48:40what
00:48:411
00:48:43natural numbers less
00:48:44equal to 4
00:48:44i can't go to negative numbers
00:48:46or 0
00:48:461
00:48:472
00:48:483
00:48:494
00:48:49so this is my solution
00:48:51first you have to write down the solution
00:48:53and then represent
00:48:55so you
00:48:56now you draw
00:48:56because my question said
00:48:58represent on the number line
00:49:00so first
00:49:020
00:49:031
00:49:032
00:49:043
00:49:054
00:49:065 and so on
00:49:08minus 1
00:49:09minus 2
00:49:10minus 3
00:49:11minus 3
00:49:12and so on
00:49:13now
00:49:13we have got
00:49:151
00:49:16so put
00:49:17circle
00:49:172
00:49:183
00:49:21and
00:49:214
00:49:22these are my solution
00:49:23so that is your complete
00:49:25now what are the things i have to make sure
00:49:28there are 2 arrows on this side showing that it is an infinite line
00:49:32next
00:49:33we are marking the points by dots
00:49:36it's a natural number
00:49:37number
00:49:37and
00:49:38next is
00:49:39we are going to have an extra element on each side
00:49:44at least 1
00:49:45you can have more than 1
00:49:46so 5
00:49:47I have got a 0
00:49:48so that means there are more numbers which are not part of the solution
00:49:52so this also you have to remember
00:49:55so this is my solution for the first one
00:49:59part 2
00:50:00part 2
00:50:02if i say x belongs to whole numbers
00:50:07then what is my solution
00:50:09one more extra number comes
00:50:121
00:50:132
00:50:143
00:50:14and 4
00:50:17so
00:50:17therefore we get here
00:50:21part 2
00:50:23so again our number line
00:50:250
00:50:261
00:50:272
00:50:283
00:50:294
00:50:305
00:50:315
00:50:31minus 1
00:50:32say minus 2
00:50:34i have got 2 arrows
00:50:35i have got the number line
00:50:37i have marked the points
00:50:38with the ruler you draw
00:50:39and then i have got one more extra number here
00:50:42so 0
00:50:431
00:50:442
00:50:453
00:50:464
00:50:47solution done
00:50:49so solving
00:50:51so solving
00:50:51writing the solution set
00:50:53and representing on the number line
00:50:55so this is what you have to remember
00:50:56part 3
00:51:00now this first
00:51:01part 3
00:51:03first let's write here
00:51:05x belonging to
00:51:08integers
00:51:08say z or i
00:51:10anything
00:51:11so what is my solution
00:51:13see i have got here 4
00:51:16i have got 3
00:51:17i have got 2
00:51:18i have got 1
00:51:19i have got 0
00:51:20but because it is integer
00:51:22we have negative numbers also
00:51:24so next negative number
00:51:25minus 1
00:51:26minus 2
00:51:27and so on
00:51:28it cannot stop
00:51:30because
00:51:31there are a lot of negative numbers
00:51:32which are
00:51:33less equal to
00:51:34infinite number of numbers
00:51:36we can say
00:51:36it just carries on
00:51:38so again my number line
00:51:39so again i have got
00:51:40minus 1
00:51:450
00:51:460
00:51:471
00:51:472
00:51:483
00:51:494
00:51:495
00:51:50so
00:51:52starts from 4
00:51:54goes on
00:51:54because
00:51:554 is the
00:51:58next
00:51:580
00:51:59minus 1
00:52:01it can carry on and on
00:52:03so how do i make
00:52:04understand that
00:52:05my solution is more solution
00:52:06more numbers are there
00:52:07you darken this arrow
00:52:09as much as you can darken it
00:52:10so this shows
00:52:12my solution goes
00:52:13my solution goes
00:52:14the arrow small arrow shows up
00:52:15the number line being an infinite line
00:52:17this shows that the solution goes up to infinity
00:52:21number of solution
00:52:22and part 4
00:52:24next one let us do
00:52:25part 4
00:52:29x belonging to real numbers
00:52:32here
00:52:32when you were
00:52:34earlier classes you learnt about representation of sets
00:52:38there are two ways you can represent sets
00:52:41one is the
00:52:42roster or tabular form
00:52:44the other is the set builder form
00:52:46right
00:52:47now real numbers
00:52:48if you think of this
00:52:52if i take this again
00:52:55between 0 and 1
00:52:57or say 1 and 2
00:52:59there are
00:53:00as small as you can think
00:53:02all possible numbers
00:53:04fractions
00:53:05decimals
00:53:05whatever you can think of
00:53:07all are there
00:53:08how can you list all those elements
00:53:10it's not possible to
00:53:11list all the elements
00:53:13so what do we do
00:53:16we have to write it in the
00:53:18this is a common error
00:53:20which is made
00:53:21listing elements of real numbers
00:53:24you cannot list elements of real numbers
00:53:27please remember that
00:53:29so therefore we get here
00:53:32x
00:53:33so we write it in our mathematical statement
00:53:35x
00:53:36less equal to 4
00:53:38x
00:53:39belonging to r
00:53:40see all the
00:53:41in one sum
00:53:42i am actually showing
00:53:43all the different ways
00:53:45we can
00:53:45we can ask for
00:53:46when you are given a sum
00:53:47they will ask you
00:53:48either natural numbers
00:53:49or whole numbers
00:53:50or integers
00:53:52and
00:53:53all real numbers
00:53:54so ma'am what are the most important points
00:53:56that we need to remember
00:53:57this topic
00:53:58i am coming to it
00:53:59after i finish the sum
00:54:00and then i will come back to it
00:54:03so part
00:54:04we are running short of time
00:54:06ok ok
00:54:09so we have got here
00:54:120
00:54:131
00:54:132
00:54:153
00:54:154
00:54:165
00:54:16so it started and we have got the
00:54:18minus 1
00:54:19minus 2
00:54:202
00:54:20so
00:54:22because real numbers
00:54:24including 4
00:54:25if it was not included 4
00:54:27then i would have put a curve line
00:54:28so here it was less equal to 4
00:54:31so from here you draw a line
00:54:33and you put an arrow
00:54:34shade it
00:54:35showing that all numbers between any number
00:54:391 2 or 2 3 are there
00:54:41so different ways we can do
00:54:43this is one of the way we can do
00:54:44we can even shade it on the line itself
00:54:47ok
00:54:47and show it
00:54:48so different ways we can do it
00:54:50so the
00:54:51so now ma'am the important points
00:54:53yeah
00:54:55can you please quickly wrap up
00:54:58because we are almost on the verge of conclusion
00:55:04we have 10 minutes
00:55:07very little time left please ma'am
00:55:10so
00:55:10important points and then we will have our assignment
00:55:13yeah there is one thing which i need to show
00:55:15just the next slide please
00:55:17there is one more sum there
00:55:19i will just explain the sum
00:55:23one more sum
00:55:24yes ma'am
00:55:25so minus 12
00:55:26yeah
00:55:27just look at this sum
00:55:28there was a question which someone had asked
00:55:30see the sum this has a 2 inequality
00:55:33quickly i am doing it
00:55:34we are short of time
00:55:35less equal to
00:55:373
00:55:38minus 4x
00:55:40less equal to
00:55:4211
00:55:42it is very important
00:55:44very very important
00:55:46point
00:55:46that when you solve an equation with 2 inequality
00:55:50never try to do it
00:55:51in the
00:55:52same step
00:55:54separate them out
00:55:56minus 12
00:55:57less equal to
00:55:583 minus 4x
00:55:59take one of them
00:56:013 minus
00:56:024x
00:56:03less equal to
00:56:0511
00:56:05so
00:56:06same as we solved the previous sum
00:56:09the same way
00:56:10we can
00:56:10solve it
00:56:11so here you solve it out
00:56:13here we have
00:56:14we solve it out
00:56:15after solving
00:56:17what do we get
00:56:174x
00:56:19less equal to
00:56:2215
00:56:23x is less equal to
00:56:2515 by 4
00:56:264
00:56:27and this one we will get
00:56:28minus 4x
00:56:29is less equal to
00:56:3111
00:56:32minus 3
00:56:33so
00:56:34minus 4x
00:56:35equals to
00:56:368
00:56:37so x again
00:56:38dividing by minus 4
00:56:40less equal to
00:56:43greater equal to
00:56:45inequality changes
00:56:46yes yes
00:56:46minus 2
00:56:47minus 2
00:56:48ok
00:56:48now the combined solution
00:56:50i am saying
00:56:51x belongs to
00:56:52ok
00:56:52real numbers
00:56:53so solution is
00:56:58now ma'am we
00:56:58yeah just a moment
00:56:59very quickly
00:57:00solution is x
00:57:02such that x is
00:57:04greater equal to
00:57:06minus 2
00:57:06and less equal to
00:57:0815 by 4
00:57:10x belonging to r
00:57:12this is how you
00:57:13write the solution
00:57:14ok ok
00:57:14now ma'am please
00:57:15assignment
00:57:15can you give
00:57:17students assignment
00:57:19yes
00:57:20so now
00:57:20slide
00:57:21ok
00:57:22the assignment is
00:57:24will very quickly come
00:57:25yes ma'am
00:57:26so we have got here
00:57:27three sums
00:57:29which is your assignment
00:57:30and you are going to
00:57:31work out in the same way
00:57:32remember these are all
00:57:33in equation with two of them
00:57:35two in equality
00:57:37remember to work them out
00:57:38in the same way
00:57:39don't try it together
00:57:41and you have seen already
00:57:42how to represent on
00:57:43real numbers
00:57:44whole numbers
00:57:45integers
00:57:45separately have shown
00:57:47so follow that method
00:57:48and also
00:57:51the solution is given also
00:57:53so that you may
00:57:56check up your answer
00:57:57the representation on
00:57:58number line is not given
00:57:59you have to work that out
00:58:00ok
00:58:01so please work that out
00:58:02and do those sums
00:58:04and do more sums
00:58:05from your books
00:58:07if you don't have your books
00:58:08I am sure your teachers
00:58:09are giving you sums
00:58:10also
00:58:11ok
00:58:12this is a puzzle
00:58:14that is being displayed
00:58:15on the television screen
00:58:18yeah
00:58:18now
00:58:19since we have done
00:58:20inequality
00:58:21I thought you might
00:58:22be interested in
00:58:26solving a puzzle
00:58:28so I hope you can see it
00:58:30there are
00:58:31four squares
00:58:32four by four squares
00:58:33right
00:58:35so we have got
00:58:36one
00:58:37two
00:58:37three
00:58:38three
00:58:38four squares
00:58:38here
00:58:39and we have got also
00:58:40row wise
00:58:41four row
00:58:42so we are
00:58:43four by four
00:58:46and now
00:58:46you can see some numbers
00:58:48and those
00:58:49inequality signs
00:58:50so it is based on
00:58:51inequality
00:58:51so the points you have to
00:58:54remember is
00:58:54you have to
00:58:56find out the unknown numbers
00:58:58two numbers are given
00:59:00two and two
00:59:01and you can use only
00:59:03numbers in a row
00:59:04or a column
00:59:05there must be no
00:59:06depreciation of numbers
00:59:07ok
00:59:07and the numbers you are using
00:59:08are one
00:59:09two three and
00:59:11four
00:59:12now there is a greater sign
00:59:14less sign
00:59:15so use those conditions
00:59:17and try to solve it out
00:59:18later we will try to give you the
00:59:20solution to the puzzle
00:59:22ok
00:59:22I hope you are successful in it
00:59:23ok
00:59:24please remember
00:59:25the few things that I have said
00:59:27one is
00:59:28when you are solving an equation
00:59:29bring all your x terms on one side
00:59:32keep your constants on the other
00:59:35solve them out
00:59:37if there are two in equation
00:59:38solve them out separately
00:59:40write down the solution set
00:59:42and then represent on the number line
00:59:45if it is asked for
00:59:47ok
00:59:48thank you very much ma'am
00:59:51thank you
00:59:54thank you
00:59:55thank you
00:59:56thank you
00:59:57thank you
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