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

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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