Simple Equations
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Simple Equations<br>Introduction to basic algebraic equations of the form Ax=B
let's say we have the equation
seven
times
acts
seven times tax
equal to
is equal to fourteen
now before even trying to solve this equation what I want to do is think a little bit about
what this actually means
seven tax equals fourteen this is the exact same thing
as saying
seven times axe
right this way seven
seven
times
times acts
the exit orange again
seven times X is equal to forty
is equal to forty nine you might be able to do this in your head you could literally go
through the
seven times tables they will seven times one is equal to seven so that won't work
seven times to
is equal to fourteen
so to works here
so you to really be able to solve it you were to be arraigned despite
trying different numbers out today
that's going to be a to
forward and do in the studios to think about how to solve the systematically because we're
going to find is as easy quake is get more and more complicated
you're not going to be able just think about it did do in your head
that's really important
but one the understand how the minute that these equations but even more importantly
ten with the actually represent
the slippery defense
seven times X is evil fourteen
in algebra
we don't right the times there when you write to numbers next to each other number next
to a variable like this
it just means that you're multiplying it's just a shorthand a shorthand notation
and general we don't use the multiplication side
because it's confusing because X is the most
is the most common terrible use of algebra and if I were right
if I were to write seven
tie-ins
atx is equal to fourteen if I write my time signer my taxable bit strange
and I look like expects or times times
so in general wondered when you're dealing with equations especially one of the variables
as a tax
you wouldn't use the traditional multiplication side
you you you might use something like this
you might use doctor personal occasions he might have seven
times X is equal to fourteen
but this is still a little unusual if you have something off the plane by verbal destroyed
seven tax that literally means
times tax
to understand how you have to for how you can manipulate this equation to solve it
let's think with visualize so seven times tax what is that
that's the same thing some his career I disagree
broader rewrite it in visual form
so seven times axe
so that will remain tax added to itself seven times that's the definition of multiplication
so so early acts
plus
plus
plus backs plus tax but see that's five X is plus attacks
so that great there is literally
seven taxes this is seven tax write their will be reread down this right here
this right here is
is seven tax
now this equation tells us that seven X is equal to fourteen
so the saying that this is equal to fourteen or destroy fourteen objects year
so with that I have
one to three four five six seven a nine ten eleven twelve thirteen fourteen
so there were six seven taxes people to fourteen things these are equivalent statements by
the reason
wired root out of this way
it so that you really understand
what we're going to do
when we divide both sides by seven to lobby the race this right here
the standard step
whatever
and what do that
he did this
we draw that last circle
so in general would never use simple find equation down to
a cold a cost-efficient is this the number multiplying very bold
so some number multiplying the very bold call it a cold fusion times of a rebel equal to
something else
we want to do is is divided both sides by seven in this case for divide both sides by
the court issued
so if you divide both sides by seven
would you get
seven times something
divided by a seven is this going to be that original something
sevens cancel out
and fourteen divided by seven is
to so you're
solution is going to be X is equal to two
but just to make it very tangible in your head
what's going on here
is we're dividing both sides of the equation by several other dividing both sides by seven
this is an equation is saying that this is equal to that
everything I do to the left hand side
I have to do to the right
if they start off being equal I I can just do an operation to one side
and have it still be equal
they were the same things about divide the left-hand side by seven
so the divided into seven groups
for their seven X is here so that's one to three
by six
sentence that's one two three four five six seven groups
but by divide that the seven groups also want to divide
i'll also wanted to buy it
the right hand side of the seven groups
one to degree four five six
so if this whole thing is people did this whole thing
that each of these little chunks that we broke into
the these talks
the seven shots are going to be the equivalent
so this child
this joint ticket a cynical to that child
this job
is equal to this job they're all equivalent talks there seven talks here seven talks years
that each
ex must be equal to to of these objects
so we get
is equal to in this case
in this case we had the
on destroying out
with there's two of them X is equal to two
let's do a couple more examples you just said it really gets in your mind
they were dealing with the equation any operation into the one side of the equation
you should do
to the other
so let me
squirrel down a little bit
so let's say I have
but said I have three
is equal to
fifteen
now once again you might be able to see unity saying this is saying three times some number
is equal to fifteen you can go through three times tables and figure it out
if you just want to do this systematically it is good to understand it systematically
say okay
this thing on the left is equal to this thing on the right
what elected to the state on the left have just X there
we have this index their our divided by three and my whole motivation for doing that
is that three times something
divided by three that degrees will cancel out I'm just going to be left with the next
three X was equal to fifteen
if on dividing the left side by three
in order for the quality this still hold I also have to divide
the right side
by degree
and what is that give us
well the left hand side
we're just going to be left with an axe
so it's just going to be a tax
and in the right hand side what is fifteen divided by three
well it is just
now you could also done this city
quaid and a slightly different way although they are really equivalent
if I start with three acts is equal to
fifteen
what can he sell
instead of dividing by three
I can also get rid of this reacted just be left with the next if I'm also applied both
sides of this equation by one third
the final to apply both sides of this equation by one third
that should also worked as a lot one-third of three is one
right we just multiplied this part right here one third times three
that is just one
one axe
one
is equal to fifteen times one-third is equal to five
and one time tax is the same thing is just acts
so this isn't a as
ex is equal five
and these are actually equivalent ways of doing it
if you divide both sides by three that is equivalent
to multiplying both sides of the equation
bye
close to one more time to make it a little bit more complicated
so let's say
I would change the variable little bit so it's that have
two
to why
to %uh I
plus
to %uh I plots
four
for why
is equal to
is he called to
eighteen
now all of a sudden it's a little harder to in your head or sing two times something
plus four times that same something
is going to be equal to eighteen so here it's hard to think about what number that is you
could try and I still apply it was one
the B-TWO times one pills four times what will that doesn't work
let's think about how to do it systematically to keep getting you might eventually get the
answer but how to do this systematically
let's visualize it so far have two wives
was that mean
it literally means I have to
I have two wise added to each other since the early
why plus why
and then to that I'm adding four wives
true that on adding four wives a juror literally for wise added to each other
so that's why it plus why plus why
plus why and that has got to be equal to eighteen
so that is equal to
that is equal to
eighteen
now
how many wise do I have here on the left hand side
how many wise do I have
I have one two three four five six lives
so you could simplify this as the six wives equal eighteen
and if you think about it makes complete sense of this is the whole this thing right here
the to why it plus the four why
is six live
so to wipe was for wife is six why which makes sense about to apples
plus for opal's of that six out polls about to wise plus four wives on that six wives
now that's going to be people to eighteen
that is going to be a will to eighty eight and now the hopefully
we understand how to do this
it has six time something is equally eighteen
if I divide both sides of this equation by six house all for the something
to divide the left-hand side by six
divide the left-hand side by a six
and divide the right hand side by six
and we are left with
why is equal to you
why is equal to three and you could try it out that's what's cool
all about equation you can always check to see if you got the right answer
but if that works to it I'm sorry
two times to the
four
times there is equal what two times three
this right here
is six
and in four times three
is twelve
six plus twelve is indeed equal to eighteen so it works out

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