L1 : Introduction - Linear Equation in one Variable , Maths, Class 8 Video Lecture

hello friends this video on linear
equations in one variable part one is
brought to you by exam feel calm no more
fear from exam topics to be covered in
this lesson our introduction equations
versus expressions linear equations in
one variable solving linear equations
with numbers on one side solving linear
equations with variables on both sides
solving equations reducible to linear
equations applications of linear
equations so let us first think of a
scenario or think of an example from
something around us let's say that you
have five candies with you or you have
five chocolates or five doggies with you
and you knew that there are total seven
candies in your home so the remaining
candles are with your little brother so
now if I ask you how many candies are
there with your little brother
now the question might sound very simple
here but can you tell me a proper method
by which you can prove that how many
candies are there with your little
brother so maybe we can go with an
approach like this that lets say that
the little brother he has X number of
candies so if he has X number of candies
and how many candies do you have you
have five candles and what were the
total number of candies at your book
total number of candies were seven so
when you look at this equation what do
you see you see that this equation
exactly satisfied the scenario because
the scenario say is that the elder
brother has five candies the younger but
brother has how many candies we don't
know but thereby 237 candies in the
house so as for that X plus 5 is equal
to 7 when X is the number of candies
with your little brother so if we solve
this equation so this is what we
call as a equation so this is an
equation and if we solve this equation
so solving an equation basically means
finding out the value of x so if you try
to solve this equation you get the value
of x as to which shows that the little
brother has two candles so basically
what did we see we see that in such
scenarios of day-to-day life we need
equations and that is why we are
learning about linear equations now what
exactly are linear equations we will get
to know that in some time but basically
this this was a very very simple example
like when I told you that there were
total 700 candies and the elder one had
5 you could have very easily calculated
in your mind that the little one would
have 2 but there has to be a method
because not every time the scenarios are
so simple so sometimes there are
situations where complex calculations
are involved so that is why we have
these equations in place so that by
solving this equations we can solve such
complicated problems of our life so here
this entire thing is called the equation
and when you look at only this part that
is X plus 5 this is nothing but an
expression now again you might wonder
how is expression how are expressions
and equations different so please do not
worry we will learn about each of them
in a lot detail so this slide was just
to tell you that why are we even talking
about equations or why are we talking
about solving an equation because we
need that to solve the daily problems
that we face so let's now talk about
expressions and equation so when we talk
about expressions what it is it is
basically a mathematical phrase with
numbers variables and operators so till
now you might have heard about the term
phrase mostly in your English grammar we
talk about phrases in English now in
mathematics also we have phrases now
what do we mean by faces raises are
nothing
when numbers variables operators they
all combine together so they form phrase
something like this let's say that we
have something like 3x plus 5 so here 3
is a number X is a variable plus symbol
is an operator and find again is a
number so this is an example of
expression similarly when you look at 4x
squared this is also an expression
because it has numbers as well as
variables you look at 5 plus 9 minus 1
this is also an expression you talk
about x squared plus y plus Z this is
also an expression so there are no fixed
number of constants now there is no
fixed number that there has to be these
many numbers or these many variables or
these many operators but wherever you
see a combination of these so that
represents nothing but an expression now
in mathematics we have a specific branch
but algebra which deals with symbols and
rules for manipulating those symbols so
he that is where we talk about these
algebraic expressions so these are also
called algebraic expressions now let us
talk about equation now the word
equation itself has this word equation
so which is has come from equal so it
actually talks about equality of
something so equation is always a
statement of equality of two expressions
now when you have two with expressions
and you have an equality symbol in
between what does that try to show for
example if we take 3x plus 5 which as I
say is an expression is equal to 1 so
now this is no more an expression it
became an equation because you have this
equality symbol now when we have this
equality symbol what are we trying to
see we are trying to say that the entire
expressions 3x plus 5 its value is equal
to 1 so that is what we are trying to
depict out of it similarly when you look
at this 4x square plus 2 is equal to 3x
so here also if you see this is an X
similarly this is also an expression but
since there is an equality sign
connecting the two so overall this is an
equation you can have equations of many
different forms many different types for
example X minus y by X plus y is equal
to 14
this is also an equation if you say 5x
is equal to 0 that is also an equation 7
y is equal to minus 9 so there could be
n number of examples for equation but
what we want to emphasize is whenever we
talk about equation there has to be an
equality symbol which equates the left
hand side at the right hand side now
normally as we move ahead you will see
that anything that lies on this side of
that equation is written as LHS that is
left hand side and this side is RHS so
for any equation LHS has to be equal to
RHS at any point in time so this is the
difference between expression and
equation because a lot of times children
remain confused that whether they are
different or they are the same thing or
if they are different then how are they
different
so all these things need to be
understood at the beginning itself so
now that we have spoken about equations
and expressions and we talked about
numbers operators variables so let us
talk about constants and variables now
in mathematics when we talk about this
algebraic equations expressions etc we
often come across many different types
of numbers variables operators so let's
very clearly understand the difference
between constants and variables now when
we talk about constants the word
constant means fix something which
doesn't change so constants are those
figures which have fixed values that is
let's say when you say - so what was - 2
is always 2 so whether you talk about 2
apples or you talk about 2 fingers or
you talk about
to friends though the number two always
signifies the same value similarly when
you talk about any number you think of
say two five nine two hundred minus
sixty-five so these are all values and
their value remains the same doesn't
matter where they are so even if you say
that even if you put them in an
algebraic expression for example if you
think of an algebra like X plus five is
equal to nine so even here nine would
always mean nine five it would always
mean five so they will not change their
value at all so they are constants
whereas when you talk about variables
variables the word itself has very so
they have varying values they have
changing values so their values changes
depending upon where they are say again
let us look at some example so let's
take the same example of the expression
that is X plus five is equal to nine now
here when you look at the value of x
what would be X X in this case would be
for right now let's say if I take up
some other equation let's say we take
another equation X plus one is equal to
two now in this equation also we have X
in this equation also we have X but here
the value of x would be one but here the
value of x is 4 so the same variable
might have different values and
different equations similarly if we
think about an equation like this X plus
five is equal to Y so here the value of
five always remains the same but if we
take X is equal to 1 in that case what
happens Y is equal to 6 if X is equal to
2 then Y is equal to 7 so you see the
value of x and y they keep changing they
are dependent on each other but their
values keep on changing so these are
called variables now variables are
normally denoted by
alphabets like ABC or XYZ or PQR or
whatever so that's how we denote them
now when we are going to talk about
these expressions like the linear
equations and when we are going to solve
them so what we are going to do is we
are basically trying to solve that
equation by finding out the value of the
variable in that equation so normally
the variables are represented by
alphabets thank you please visit exam
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