Maths Simple Equation part 5 (Solving an Equation) CBSE Class 7 Mathematics VII Video Lecture | Extra Documents & Videos for Class 7

hello friends this video on simple
equations part 5 is brought to you by
exam feel calm no more fear from exam so
now that we learned how do we set up
equations it's time that we start
solving them as well because only when
we solve equations we are actually able
to solve the problems so how do we solve
this equations now whenever we talk
about solving an equation we mean we are
going to find the values of the
variables such that left hand side is
equal to right hand side so only then we
call them the solutions for that
equation so let us take an example so
let us take this example so let's say
that we have an equation 3x plus 1 is
equal to 7 now if I ask you to solve
this equation that means what you need
to do you have to find out that value of
x for which left hand side is going to
be equal to right hand side so let us
try different values of X let us say we
put X is equal to 0 so what will happen
what would be left hand side left hand
side would be 3 into 0 plus 1 which is
equal to 1 so is left hand side equal to
act our right hand side because right
hand side is equal to 7 so 1 and 7 are
equal
no so that means X is equal to 0 is not
the solution ok now let's try it with X
equal to 1 so what would be our left
hand side it would be 3 into 1 plus 1
that is 4 his left hand side equal to
right hand side no therefore X equal to
1 is also not the solution now let's try
with X is equal to 2 so what do we see
in this case left hand side is 3 into 2
plus 1 CH 3 to the 6 plus 1 that is 7 is
left hand side equal to right hand side
yes therefore X is equal to 2 is a
solution for this equation so X equal to
2 is the solution for this particular
equation now again the solution for
different equations will definitely be
different now let it and
type of method where we keep trying with
different different values of the
variables that is called trial method
that is we keep trying hit and ran with
them we use we take up one value we try
it we fail we take up another value we
feel we didn't take up another value
until and unless we'd reach to the right
value so this this this is just to show
that there are only certain values for
which the equation will be true for
which the LHS will be equal to RHS let
us take one more example so let's say
now we take a different type of equation
let's say 1 by 3 y plus 3 is equal to 3
so in this case let's try with Y is
equal to 0 so when you put y is equal to
0 LHS is equal to 1 by 3 into 0 plus 3
which is equal to 3 so this 3 is equal
to RHS so LHS is equal to RHS therefore
Y is equal to 0 is the solution for this
equation let us take one more example
let us consider this equation 3x minus 1
is equal to 2x so in this case you have
the one variable that is X but you have
two terms involving this variable right
so let's see how do you do this so again
let's first try with X is equal to zero
so for X is equal to zero LHS is equal
to 3 into 0 minus 1 which is equal to
minus 1 and what would be Anytus RHS
will be equal to 2 into 0 that is 0 so L
it is minus 1 RHS is 0 so LHS and RHS
are not equal therefore X equal to 0 is
not the solution now let's try with X
equal to 1 so in this case LHS will be
equal to 3 into 1 minus 1 that is equal
to 2 and what would be our H's iessons
will be equal to 2 into 1 that is also 2
so LHS is equal to RHS therefore X is
equal to 1 is a solution for this
equation so this is basically what we
mean by solution of an equation now the
question is how do we solve an equation
now it
definitely not a nice idea to use this
trial method that is we keep prying
numbers because it is also possible that
for some equation X is equal to 25 is
the solution so do you think it is
feasible to keep trying from X equal to
0 or than 1 2 3 4 and so on
definitely not so there has to be a
smarter way to solve equations so how do
we solve the equation now just one thing
that you need to remember while we try
to solve an equation is that whenever
you are trying to solve an equation make
sure that the balance of the equation is
maintained now what do we mean by
balance of an equation now any equation
let's take an example let's take this
equation as an example 3x plus 9 is
equal to 1 so let's take this equation
as an example any equation will have an
equal sign and therefore any equation
will have a left-hand side and the
right-hand side 2 under any condition it
is very important that the left-hand
side and the right-hand side remain
equal so they need to be equal under any
situation this balance should not be
disturbed now let us say if you have
this equation 3x plus 9 is equal to 1
and now we say that we want to solve
this equation we want to find the value
of x but we do not want to follow the
heater drag method so how do we go about
it now 1 approaches what we do is for
these kind of equations whenever you
perform any kind of operation on one
side do it on the other side as well for
example in this equation let's say if we
say that let's subtract 9 on both sides
subtract 9
from both sides why from both sides
that's because when you are removing
nine from left hand side that means the
overall value of the left hand side is
decreasing now if you do not remove nine
from the right hand side so the right
hand side will remain here so what is
happening the balance is getting
disturbed but do we want to disturb the
balance no so that's why we will
subtract 9 on the right hand side as
well so what do we get now plus 9 minus
9 this would become zero so we are left
with 3x on the left hand side and what
do we have on the right hand side 1
minus 9 that is minus 8 okay now what is
our aim our aim is to find the value of
x so we just want that somehow we should
have only X on the left hand side like
in that case we will get the value of X
because X is equal to something that is
what we want so our problem statement
here is we want to find the value of x
so if somehow we can remove the streets
how can we get rid of this 3 so for that
again what we do we divide left hand
side by 3 so if you divide left hand
side if you divide 3 eighths by 3 then 3
& 3 will cancel out so you will be left
with X but if you are dividing left hand
side by 3 what are you supposed to do on
the right hand side on the right hand
side also you have to divide by 3
otherwise again the balance will get
disturbed and we do not want to disturb
the balance so divide 3 on both sides so
what happens when you divide 3 on both
sides it becomes like this 3 X by 3 is
equal to minus 8 by 3 so 3 3 will cancel
so we get X is equal to minus 8 by 3 and
what is this this is the solution of
this equation right finding the value of
the variable for which this equation
will hold true that is the solution of
the equation now if you want you put
this value of x in this equation so put
X is equal to minus 8
three in the equation so what do you get
you get three in two minus 8 by 3 plus 9
so 3 3 will cancel this is minus 8 plus
9 which is equal to 1 so this is the
value from the left-hand side and the
right-hand side is also 1 that means yes
X is equal to minus 8 by 3 is the
correct solution so what we actually did
what is the approach that we followed
the simple approach that we follow else
whatever we do certain operations on
both left-hand side and right-hand side
why do we do these operations so that we
can get the value of x so earlier we had
3 X plus 9 on the left hand side and we
wanted this to become X so to get X from
that tree X plus 9 we do some operations
we do some subtraction some divisions
and only then we get X the only point
you need to remember is whatever
operation you perform on one side you
need to perform it on the other side
also because at any point in time
left-hand side should be equal to right
hand side and when left hand side and
right hand side is equal we see that the
equation is balanced so the balance is
maintained the moment the balance is
disturbed everything becomes incorrect
so in with that approach you will not be
able to reach anything so at any point
in time the balance needs to be
maintained so this is the concept or
this is the logic behind solving an
equation now what we will see is how can
you do it in an easier way we will
basically do the same thing but I will
tell you some shortcut tips by which you
can very quickly solve equations but the
concept will remain the same thank you
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