Time to kill PART 2

oh this is the part i hate.
DO I HAVE TO

arvin's conscience : "DUHH!!!"

FINE!

hmph.

on to the harder part.
i already dealt with equations like..
"12 = 1 + x"
and..
"12 = x - 1"

now, how do we find the value of "X" if we have an equation like,

3x = -6

now. the goal is still the same.

Find the Value of the variable.

we have 3 set's of x's that are equal to (-6)
this is how it would look like in algebra tiles.


now, our problem here is that we have 3 sets of x's and the value of the total of those 3 sets is on the other side.
now, we still need to isolate the x's
since we have
3x = -6
we have to cancel out the co-efficient for x
how? by dividing it.
3x is equal to 1x or simply, x.
3
remember the what u do to one side u do to the other rule?
well.. since u divided one side by 3 (to cancel out the co-efficient) we divide the other side by 3 too.
so we have

3x = -6
3
it would look like this in algebra tiles,


the result would be,



or in plain arithmetic

x = -2

get it? easy isnt it?
okay.

now let's flip it.
say we have an equation

x = -2
3

Now, what we know is that 1/3 of the variable x is equal to -2
to get the FULL value of the variable "x"
we have to multiply it by the number the variable is being divided by. in this case, that number is 3.

so we multiply BOTH sides of teh equation by 3.

and because we were dividing the variable by 3, multiplying it by 3 nullifies BOTH of the operations, leaving it simply as, X. and viola, we have isolated X.
but since we used teh process of multiplying (x/3) by 3, we have to do the same thing to the other side of the equation. therefore, we multiply (-2) by 3.
after all the calculations, the equation would look something like this...

x = -6

there.
i have explained all four of the operations. but the next.. is the multi operation equations. (WOW! it rhymed~!) but unfortunately. i dont think im in the mood to do that today. hahaha.. sorry guys. cya later.

Time to kill = Time to catch up

HELLO PEOPLE!It's been a while since I think ANYONE got on this site to make a post and no, I don't blame Mrs. Armstrong, she has enough on her mind. And I think we should be responsible enough to be able to take care of this. I mean,this is for our good.
ANYWAY..BACK TO Math. In my next posts, im going to TRY and catch up to what we did. aights?kk. be ryt back, preparing my notes.

Number 1

What we are doing in math now is solving EQUATIONS.
now. the question is not "What's the answer", "it's what's the value of X?"

let's say we have an equation where the ask us to find the VALUE of the variable X.

let's say we have..

"12 = 1 + x"

now the question is what is the value of x?
now take a look at the equation. looks hard? well. visualize this.
it's on a see-saw kind of thing. the "=" sign is the middle of it.
the numbers are the things on either side.
in algebra tiles, this is what it would look like.


now. The balance is "Balanced" meaning whatever is one the left side,
is equal to whatever is on the right side.
now. To get the value of X. The objective here is. ISOLATE the VARIABLE.
how do we do that? We take off whatever is with the "X"
now we cant just take it away. We need to take it away using Zero models.
to make a Zero Model with (+1) we need to add it's opposite to it. so we add (-1) to make it a Zero-Model. But there's a rule for it. to keep the two sides balanced, we need to do the same thing we did to the other side.
so if wee added a (-1) to one side, we add (-1) to the other one too.
now.
our question is now
"12 = 1 + x"
we already know how to make zero models. so to get the "X" by itself, we need to delete the (+1)
near it. (by making zero models of course.)

so our equation now goes, +12 -1 = 1 -1 + x
notice that i added a -1 to both sides. this is to KEEP IT BALANCED.
this is what it would look like on algebra tiles.

now that we cancelled out the +1 on the side with the variable. the is nothing with the variable.
now that equation reads..
11 = x

there, we found out what "x" is equal to.

that's basically how you do it. but that's only with addition & subtraction.
if the equation was,

"12 = x - 1"

you would still make zero models to isolate the variable x.

12 +1 = x -1 +1

the zero model on the side where the X is cancels out the "-1 and leaves nothing but the variable X behind. now, on the other side of the equals sign, we did the same thing to keep the balance.
because we added on (+1) to the side with "X" we have to add (+1) to the side with the numbers in it too. JUST TO KEEP IT BALANCED.
the result would be..

13 = x

there, i have finshed my post on that part. i'll be posting the next part shortly. the one abou multiplication and division.