How to get an Equation from a Solution? Video Lecture - Class 7

hello friends this video on simple
equations part nine is brought to you by
exam feel calm normal fear from exam so
with this we solved a couple of
equations and we got an idea about how
do we actually solve equations now the
question is here till now we were given
equations and we will finding its
solutions now do you think that it is
possible to do it the other way around
that means if I give you solution for
equation and I ask you to find that
equation we will be able to do that
sounds crazy right but yes you can do
that let's say that you are given an
equation 3x minus 2 is equal to 4 so and
and I asked you to find the solution for
this equation so by now if you already
know how to find solution so very
quickly you will be able to find the
solution for this equation so how do you
find the solution for this equation let
us look at in detail so how do you find
the solution so 3x minus 2 is equal to 4
so first we will move to 2 right hand
side so this becomes 3x is equal to 4
plus 2 so you will say 3x is equal to 6
therefore you can say X is equal to 6
divided by 3 3 through 6 therefore X is
equal to 2 is a solution for this
equation so this is simple now let's say
that if instead of giving the equation
if I give you the solution so if I tell
you that X is equal to 2 is a solution
for an equation find out that equation
so do you think that you will be able to
find out that equation it sounds good
but actually you can you actually can
find out the equation for which X is
equal to 2 is a solution so let us see
how do we do that so let us assume that
you are given a solution like this X is
equal to 3 so this is a solution that is
given to you and I asked you to make
equations out of it now basically you
look at any solution the solution it
also an equation in a very simple form
here also you have a left-hand side you
have a right-hand side you have an equal
sign it is just that you have performed
all the operations therefore you do not
see the plus minus multiply or divide
otherwise a solution in itself is also a
very simplified version of an equation
now let us say if you multiply 2 on both
sides of this equation so what do you
get you multiplied 2 on both sides the
left-hand side becomes 2x right-hand
side becomes 6 so 2x is equal to 6 what
is it this is an equation so we have
arrived at an equation from a solution
now let us say in we add 3 on both sides
so once you add B on both sides what
happens left-hand side becomes 2x plus 3
right-hand side becomes 9 what is this
this is again an equation Thanks so 2x
plus 3 is equal to 9 is also an equation
now let us say that we add something
else let's say we add 10 on both sides
what do you get
it becomes 2x plus 3 plus 10 that is 13
is equal to 19 what is this this is also
an equation right now let's say that I
multiply both sides by 3 so you multiply
3 on both sides so what what what again
do you get it becomes 3 into 2x plus 13
and on the right hand side 3 into 19 is
57 and what is this this is also nothing
but an equation you see all of these
satisfy the definition of equation and
that is why they are equations right so
what do you observe you observe that if
one solution is given we can create
multiple equations from that solution
now not only these equations let us say
if we start from the beginning and if we
now multiply both sides by 3 so what do
we get
instead of 2x equal to 6 we get 3x is
equal to 9 now let us see if you
subtract 1
on both sites so what do you get you get
3x minus 1 is equal to 9 minus 1 that is
8 so for the same solution X is equal to
3 you also find an equation like this 2x
plus 3 equals to 9 and you also find an
equation like this that is 3/8 minus 1
is equal to 8 so basically the
conclusion is that multiple equations
can be created from one solution so if
you had given one equation if equation
is given you get only one solution for
that equation so basically the number of
solutions for an equation is limited but
when the solution is given how many
equations can you make you can actually
make multiple equations so for one
equation you have a specific solution
but for one solution you have multiple
equations so that is one beautiful thing
that we conclude from here and I hope
you also got to understand that how
exactly do we create solutions how
exactly do we create equations from
solutions here are something basically
follow the same way that we perform have
operations on both sides we multiply by
the same number on both sides we add the
same number on both sides we subtract
the same number of both sides and that
is how we obtain equations from solution
so try this out construct three
equations starting with X is equal to
minus 2 so this is the solution which is
given now let's say you multiply by 2 on
both sides so then you multiply by 2 on
both sides the LHS becomes 2x and the
RHS becomes minus 4 so 2x is equal to
minus 4 this is one equation now let us
say that you add 3 on both sides so what
happens left-hand side becomes 2x plus 3
and right-hand side becomes minus 4 plus
3 therefore this becomes 2x plus 3 is
equal to minus 1 so this is also an
equation so let's say this is the second
equation that we create
4x is equal to minus 2 now let's say
that from this equation that is 2x minus
4 after this we subtract 1 on both sides
so what do we get we get 2x minus 1 is
equal to minus 4 minus 1 that is 2x
minus 1 is equal to minus 5 so this is
yet another equation now if you want to
verify what you can do is you can try to
find the solution for each of these 3
equations and in all the cases you will
find that their solution is X is equal
to minus 2 so this is how we create
equations from solutions thank you
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