Reducing Linear Equations in Linear Form (Method 2) Video Lecture | Advance Learner Course: Mathematics (Maths) Class 7

hello friends this video on linear
equations in one variable part 5 is
brought to you by exam for your calm no
more fear from exam so let us now move
ahead with the next type of equations
that we will learn to solve so these are
equations which are reducible to linear
form so here the equations would still
be linear equation but they will not
appear in the same conventional form of
linear equation so the way they will
appear to us would in good-look complex
but we will see how we can reduce them
to the usual form of linear equation so
whenever you find an equation of this
form where you have a numerator divided
by denominator is equal to a numerator
divided by the denominator we had these
numerators and denominators and as have
these expressions like they could be
anything like 2x plus 3x plus 9x plus
1by plus 2 so anything of this sort so
whenever you have an equation of this
form something like this let's take an
example 2x plus 3 divided by X plus 9 is
equal to 1 by 2 or sometimes even on
this side you might have these kind of
expressions so when you have an equation
of this form now when you look at this
equation it doesn't look that simple
like the usual linear equation right so
you feel that don't know what to do so
the only thing that you need to do in
this case is your first step should be
to cross multiply now what do we mean by
cross multiply
cross multiply means you multiply the
denominator on the right hand side to
the numerator of left hand side
similarly you multiply the denominator
of left hand side with the numerator on
right hand side so that is called cross
multiplication so in this case what will
happen in that is 2 into 2x plus 3 will
be equal to 1 into X plus 9 so that is
what you will get so in this case 2 into
2x would be 4x plus 2 into 3 would be 6
and this side it would be X plus 9 now
so basically you know what are we doing
when we are cross multiplying now
basically
we are cross multiplying we are actually
multiplying this denominator on both
sides it is the same thing if you
multiply X plus 9 on both sides now why
are they doing this cross multiplication
to keep things simple because every time
when you have to multiply something on
both sides first you will think what I
have to multiply then you will multiply
that so it will take more time in this
case you just know all you need to do is
you need to cross multiply multiply you
the denominator on the other side so
this is what you get now you put all the
variables on one side like this and all
the constants on the other side so you
get 3x is equal to 3 or X is equal to 3
divided by 3 that is equal to 1 so X is
equal to 1 would be a solution for this
equation so you see even though the
equation looked complex but we could
very easily solve it now one important
thing that needs to be noted here is
this rule is applicable only for
equations in this form and this rule is
strictly not applicable for different
forms of equation for example if you
have an equation of this form X by 2
minus y1 by 5 is equal to X by 3 plus 1
by 4 now is this equation in this form
this equation is numerator by
denominator minus numerator by
denominator but here we said it should
be numerator by denominator equal to
numerator by denominator so in this case
this rule will not be applicable to you
should not start cross multiplying here
so this will not be happy table for this
case however if you have an example like
X minus 1 by 2 is equal to X plus 1
divided by 12 so here you see it is in
the same form numerator by denominator
numerator by denominator so here this
rule would be applicable so you can
directly cross multiply again let's take
one more example 6x plus 1 divided by 3
plus 5 is equal to X minus 9 by
so in this case on the right hand side
it is in the form of numerator by
denominator but on the left hand side it
is not in that form here you have
numerator by denominator plus a number
so therefore here also overall the rule
will not be applicable
so with this examples what I am trying
to tell you is where exactly can you
actually apply this concept of cross
multiplication to solve the equation so
now you might say that okay fine so we
will be able to apply this concept only
where this particular form holds true
but what about all these complex forms
because even these look look more
complex so how are we going to solve
them so how are you going to solve these
complex equations thank you please visit
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