algebra

[shell pendant]

Practicing algebra topic, I need help.
I need someone to cheek my work and help me do the second question, because I have no idea where to start

[ancient lava]

I cheeked your work and I don’t think it is correct

Is this the question?

[shell pendant]

Yeah......

[shell pendant]

Yes this is the question

[ancient lava]

ok nice

[shell pendant]

By the way thank you for helping me last yr, i got second best class in school now

still ashame my algebra is slow

[ancient lava]

oh wow, happy to hear that

[ancient lava]

Nah, I’m gonna give you so much examples that you are gonna be killing it

[shell pendant]

IM READDDYYY

[ancient lava]

do you agree with this

[shell pendant]

Yes i do

[ancient lava]

so what would be the answer for this

[shell pendant]

6, x²

[ancient lava]

Yep! Exactly

6/x^2

[shell pendant]

Woahah

[shell pendant]

Aight

[ancient lava]

can you simplify this?

[shell pendant]

let me try.
1/3 x y^-1

I dont know what happend to x if x-x

[deep ledge]

you deserve this fucking helpful role so much

[ancient lava]

Lol

[shell pendant]

Agree2

[ancient lava]

Umm, kinda correct but the final answer should have been 1/3y

in order to simplify a fraction, you cancel out things that are the same

[shell pendant]

Ohh okay but for y, 1-2 =-1? that dont count?

[ancient lava]

yes that is right

[shell pendant]

Oh nevermind you changed its shapes

[ancient lava]

You are gonna get what I mean

[ancient lava]

Ok you probably do agree with this

[shell pendant]

Got it

I agree

[ancient lava]

ok nice

I’m pretty sure you already know these stuff

just reviewing them!

[shell pendant]

Im not the best in slashing fraction thing but yes I agree

[shell pendant]

Got itt

[ancient lava]

Now we are left with this

[shell pendant]

3y

[ancient lava]

Yes!

exactly

[shell pendant]

wooooooo

[ancient lava]

Or

Does that make sense?

[shell pendant]

Kinda, yes

[ancient lava]

What is the final answer for this?

[shell pendant]

2x+2/x

?

Oh wait

2x+2/x

2+2

4

I think i messed up

[ancient lava]

Yeah kinda

but let’s not expand anything

You multiplied 2 to the x+1

When you see things that are exactly the same in a fraction

you can simplify them

wait a second I will be back

[shell pendant]

Okay take your time, im gonna redo this one in minutes

[ancient lava]

I’m back

[shell pendant]

ehat the hexk

[ancient lava]

What do you think can be simplified here?

[shell pendant]

A

[ancient lava]

Exactly!

and the final answer for it

[shell pendant]

final answer 2

[ancient lava]

Yep!

[shell pendant]

Wargh

[ancient lava]

now let’s get back to the previous question

let’s consider x+1 as B

so x+1 = B

[shell pendant]

What happens after this

[ancient lava]

ok you can’t do that

[shell pendant]

Aaa what did i do wrong

[ancient lava]

because the nominator has addition and stuff

you can only cancel out

when they are being multiplied

but let me give you an example to clear this thing up

[shell pendant]

Alright then

[ancient lava]

Take a look at this example with numbers

without canceling or anything

it would be like this right?

[shell pendant]

Yes.

[ancient lava]

ok and as you know, 6/3 is 2

now let’s simplify the way you mentioned

Cancel out 2s

you get 4/1

which is 4

it’s not the same answer

the same way we can’t simplify 2s here, you can’t cancel out 2x

let’s say x+1 = a

And as you mentioned, As cancel out and you get 2

[shell pendant]

Am i doing it right nowwwww

[shell pendant]

Yes i got 2

[shell pendant]

Ok

[ancient lava]

Ok but sorry to say the way you wrote is not correct

2x + 2 does not equal 4x

in fact

2x * 2 = 4x

[shell pendant]

Oh okay

Its good, im learning and im the one sorry for my lack of knowledge

[ancient lava]

You will learn it fast

but just remember this

[shell pendant]

I cant understand how youre presenting this irl, whats that *

[ancient lava]

you can cancel out things that are the same

[shell pendant]

OHH

[ancient lava]

2x times 2 equals 4

[shell pendant]

My bad i wasnt paying closer attention to the question

[ancient lava]

ok np

now simplify this one

[shell pendant]

ANSWER IS 2

[ancient lava]

Yep!

[shell pendant]

YEA

[ancient lava]

As you know, the same way you can multiply 2 to the inside of the parentheses, you can factor out the same way

[shell pendant]

Got it.

[shell pendant]

9x/x

=9?

[ancient lava]

Try to use this 🤔

[shell pendant]

YO ITS 3

YAAAAAAA

[ancient lava]

YEEES!

Let’s make it harder!

[shell pendant]

DO IT, gotta practice real hard before tommorrows test

[ancient lava]

yes!

[shell pendant]

IS 2

[ancient lava]

YEP

now even more harder?!?

[shell pendant]

YEAH MANN

[shell pendant]

3 💯

[ancient lava]

YOU ARE COOKING 🔥🔥

[shell pendant]

LET ME COOKK 🔥

[ancient lava]

what do you think you can cancel out?

[shell pendant]

I think i can cancel out (x-1)

2 of them

up and down

[ancient lava]

hmm, x+1 or x-1 🤔

[shell pendant]

OH

X+1

[ancient lava]

Yes!

now the final answer

write and send a picture so I make sure there is no mistake

[shell pendant]

this this this?

[ancient lava]

After you cancel out, you get 2/x-1

(You have mis read it but alright)

but

in fact

[shell pendant]

Oh i did misread it

[ancient lava]

2/x-1

Is the final answer

[shell pendant]

this gonna be the reason of my lost in marks. Im gonna fix it

[shell pendant]

OKAY

[ancient lava]

also before we go on to the next ones

I want you to fix some stuff

for exampl

x + 2 does not equal 2x

3x + 5 does not equal 15x

x + y does not equal xy

so try not to make these mistakes again

[shell pendant]

What does it equal to?

[shell pendant]

Like this one

[ancient lava]

you can’t simplify more than that

that’s the final thing

and also you might be asking why that is??

[shell pendant]

Ohhh okay

[shell pendant]

Yea

[ancient lava]

consider x + 2

[shell pendant]

Its still algebra and idk why it cant be like how i did

[ancient lava]

x+2

if it is 2x

then it means 2 times x

So we say

x + 2 = 2x

now let’s give x, a value, you tell me

pick a number

[shell pendant]

7

[ancient lava]

Ok nice

if you put it there

you get

7 + 2 = 2*7

9 = 14??

[shell pendant]

no.

[ancient lava]

so as you can see, the idea of writing x+2 as 2x is not correct

because we just proved that it was wrong

x+2 will stay x+2

[shell pendant]

I guess it dont make sense

Thank you, i got it

Now lets move on to ramen

If u think im ready enough

[ancient lava]

you mean the question you sent?

Sorry my English is not that good so by that I didn’t really get what you meant

[shell pendant]

I didnt really get which question you meant by my question

[shell pendant]

Oh

Oh i said ramen, referring to spicy questions

[ancient lava]

ah ok

[shell pendant]

synonym with hard questions

[ancient lava]

got it

ok now let’s solve some more

[shell pendant]

Alright

[ancient lava]

this is a little too hard but I’m sure you can do it!

Try to simplify

[shell pendant]

Is the answer 1?

[ancient lava]

DAMN

[shell pendant]

YAYYYY

[ancient lava]

YES IT IS

[shell pendant]

MY MUSCLES R GETTING BIGGAR💯

[ancient lava]

Umm let’s not expand alright?

[shell pendant]

Alright ill try not to

[ancient lava]

Try to do it once more with factoring

factor out as much as you can

https://cdn.discordapp.com/attachments/1223967628326994071/1223983567692894291/55BDB778-B982-4F26-8996-AB3F18663610.jpg?ex=661bd687&is=66096187&hm=1e2d0a997c9470070ea72b0cd3d559ef9ed0cdef0677c5f9ac7599a3424ffdd8&

[shell pendant]

Ill remmeber this

[ancient lava]

try to use this method

[shell pendant]

Okay got it

I didnt notice u said once more

I got it

[ancient lava]

oh lol

Yes!

[shell pendant]

My baddddd

[ancient lava]

now thats what I’m talking about

[shell pendant]

Sorrrryyyy I DIDNT REALIZE U SAID ONCE MORE

[ancient lava]

No problemmm

[shell pendant]

Yayyush

[ancient lava]

the thing you just sent is completely correct

but the previous one was completely wrong

[shell pendant]

Got youuu

[ancient lava]

Alright one more thing before we go on to other examples

[shell pendant]

Thank you thank you

[shell pendant]

Okk

[ancient lava]

you can’t simplify things when they are being added

like 2x+3/2x+1

you can’t cancel out 2x

this is also one rule

[shell pendant]

Oh because it will become non algebra is it

?

[ancient lava]

umm idk what that means but it’s against the rules of algebra

[shell pendant]

Because if i did cancel out 2x from 2x+3/2x+1, ill get 3/1, final answer is 3 and thats not algebra anymore

[ancient lava]

yes it’s not correct

[shell pendant]

Okay i get it

[ancient lava]

also great to see yo could expand (y-2)(x+2)

I have met people who can’t do such a thing on high levels of math

keep it up!

[shell pendant]

Got a great teacher so yea

thank youuu its all you😭

[ancient lava]

I mean, you knew expanding before me so

yeah thanks to the person who taught you well on expanding

Because it’s very important thing!

[shell pendant]

Damn okay, i get it

[shell pendant]

YES IT ISSSSSS

[shell pendant]

I dont think the expand thing is high, its been around for years from my learning and its just me that cant do factors until you taught me

[ancient lava]

Yes but I meant that even tho it’s not a high level thing,some people don’t remember/ haven’t learnt them

Alright whatever

simplify this one and we will go on with the next level of questions

[shell pendant]

x-5/3 ..?

[ancient lava]

YES!

that is correctt

[shell pendant]

YAA

[ancient lava]

what do you think this equals to ?

[shell pendant]

=x+2 ?

[ancient lava]

Yep!

[shell pendant]

okay!

[ancient lava]

Also note that (x+2) can be written as x+2 and there is no difference between them!

[shell pendant]

Got it

[ancient lava]

Ok nice

remember this thing

because you are gonna have to use it with this example

[shell pendant]

Even if theres ² or etc outside of those brackets, we can erase the brackets?

Oh nvm my bad

[shell pendant]

I will remember this

[ancient lava]

Ok nice, this one turned out to be a little too hard, let’s see if you can do it

[shell pendant]

2/5(x-2)

2/5x-10

I dont know what to do after

[ancient lava]

STOOP

[shell pendant]

Have answers be left like this?

WHAT

[ancient lava]

THATS CORRECT

[shell pendant]

OH

WARGGHHHHH

YAYYY

[ancient lava]

THATS THE FINAL ANSWER YES!

as you can see there is nothing else to simplify, so you leave it that way

[shell pendant]

KICKING MY FEET WOODJ

[shell pendant]

I seee thank you

[ancient lava]

Alright now let’s solve things that are similar to the problem you sent!

[shell pendant]

okaaayyyyy!

[ancient lava]

What is the different way of writing a^2 - b^2

[shell pendant]

a x a - b x b ?

[ancient lava]

Yes that’s also one way

but

[shell pendant]

but!?

[ancient lava]

the useful way of writing it is this:

[shell pendant]

You factored it?

[ancient lava]

It comes from expanding

Since you are good at expanding

(a-b)(a+b)

expand this and tell me what you get

[shell pendant]

a²-ba-ba-b²? Im getting less confident

I think i mixed ² and 2 IDK

[ancient lava]

in fact, you did everything right!

[shell pendant]

glad😭 thank you

so whats next

[ancient lava]

This thing is very important

use it on this example

[shell pendant]

saving everything important as you said

[shell pendant]

=a+b

[ancient lava]

yep!

What about this one 🤔

[shell pendant]

I couldnt see where this question can be related to the previous important thing were saying, i got
x-4/2

[ancient lava]

Ok you did something similar the thing here, which is not correct

https://cdn.discordapp.com/attachments/1223967628326994071/1223990924669882389/Untitled39_20240331214548.png?ex=661bdd61&is=66096861&hm=fe5cecc78eaed443104ffa52e0912411b85d81b11cf628e0f51ba42dda10346f&

let me tell you how it is simplified

as you know

4 = 2^2

[shell pendant]

Yes

[ancient lava]

As you can see, we have something similar to a^2 - b^2

We apply the rule a^2 - b^2 = (a-b)(a+b)

Now you probably know the next step, you cancel out x+2 and you get x-2!

[shell pendant]

=x+2 😔

Wrong symbol

[ancient lava]

yea

[shell pendant]

=x-2

[ancient lava]

Now try to simplify this one

[shell pendant]

okay

[shell pendant]

=x+3

[ancient lava]

Yep!

That is correct!!

[shell pendant]

youre way of teach is so skilleedddd

[ancient lava]

🤔

seems like this one is too hard 💀

[shell pendant]

No kidding.

I know i did this wrong clesrly..

4(x+3)/2

teach meeeee

[ancient lava]

can you tell me the answer for (2x)^2

[shell pendant]

4x

[ancient lava]

Yes! It is 4x^2

[shell pendant]

wow okay

[ancient lava]

ok nice, can you guess the next step?

[shell pendant]

Factor it? Like (x-2) (x+2), i dont know

I dont think that made sense

[ancient lava]

yes! It’s gonna be something like that!!

[shell pendant]

aaaaaahhh then its not the next step

What is it?

[ancient lava]

a^2 - b^2 = (a-b)(a+b) as you just said

and now we got

(2x)^2 - 3^2

(2x-3)(2x+3)

:)

and now as you know

2x-3 are the same on both nominator and denominator

you cancel them

And you get 2x+3 !

does that make any sense?

[shell pendant]

it does make sense

Alright

Im getting it

[ancient lava]

🔥🔥🔥

[shell pendant]

Im stuck

[ancient lava]

alright what step

well

You have changed everything there

But I see you have tried to write (3x)^2 which is nice

[shell pendant]

[ancient lava]

You are actually so close the answer

just please delete everything

and write

(3x)^2 - 4/3x+2

[shell pendant]

okay

[ancient lava]

and now what do you think you can do to use a^2 - b^2

Or let’s say how you can (3x)^2 - 4 in the form of (a-b)(a+b)

[shell pendant]

3x²-4
form in (a-b)(a+b)
=?

there wasnt a value for x before and now i dont get it

[ancient lava]

There is no need for value

let me solve this one for you so you get what to do

[shell pendant]

Okay

[ancient lava]

As you know, 9x^2 is the same as (3x)^2

And 4 is also 2^2

We can somehow see how we can use the rule of a^2 - b^2 = (a-b)(a+b)

and then you know what to do

I’m pretty sure it didn’t make that much of sense

but

let’s stop for 10 minutes to rest

and please think about nothing and just try to relax

[shell pendant]

No, im trying to speedrun my study for tommorrows test and no worry, im getting the hang of it and it makes sense to me more now i think

[ancient lava]

Umm ok

then I’m here

let’s solve more examples!

[shell pendant]

Yes

but

You can rest first

Actually lets do the 10 minute rest, i need to settle some things i forgot

[ancient lava]

nah I said that cuz I thought It was kinda hard to do it continuously

[ancient lava]

Ah ok ok

@shell pendant

[shell pendant]

Im here

[ancient lava]

sorry to say that I gotta go for like 35 minutes

[shell pendant]

Right now? Sure

[ancient lava]

But you can do these if you want

To review everything we discussed

[shell pendant]

I will do these

[ancient lava]

Nice!

[shell pendant]

Alright alrightt

[ancient lava]

I will be back soon

[shell pendant]

Okayy

[ancient lava]

Alright I’m back

[shell pendant]

I finished answering

A) 4y+8
B) 1/3 x
C) m+2
D) y-3/x+2

correct me when im wrong

[ancient lava]

HOLYYY SHTT

EVERY

SINGLE

[shell pendant]

DID I GET IT

[ancient lava]

ONE OF THEM IS CORRECT

[shell pendant]

WAARRGHHH YOURE THE COOLEST TEACHER EVER

[ancient lava]

damn you did a great job!

[shell pendant]

Thank you alien

[ancient lava]

No problem!

[shell pendant]

Im happy for my progress and you did the best either

is that all for tonight?

[ancient lava]

🔥

[shell pendant]

it hit 12 am

[ancient lava]

oh you gotta sleep

umm

Let’s practice a^2 - b^2 and we will be done

[shell pendant]

Errrrr

[shell pendant]

Okay aure sure

[ancient lava]

For like 15 minutes

[shell pendant]

Alright im cool with it

[shell pendant]

(a-b)(a+b)
(x-1) (x+1) / x+1
=x-1

I did (x-2) before but i think that looks messy so i changed it to accordingly to the logic

I think this is wrong though

[ancient lava]

yep! That is right!

[shell pendant]

Okay!

[ancient lava]

Before I give you harder ones

tell me

try to write everything I mention here like 4x^2 = (2x)^2

9x^2 = ?

[shell pendant]

3x^2?

[ancient lava]

(3x)^2

the point I want you to reach here is to be able to write them like a^2 - b^2 to be able to use the rule

[shell pendant]

but why are 9² the same as 3² when they give different value if we calculate it? I thought 3² is because we get 9 from it

i probably dont get it still but ill manage

[ancient lava]

yes 3^2 will turn into 9

3x^2 means only x is squared

but (3x)^2 means both of them are squared

which is the same as 9x^2

[shell pendant]

if we want to use the rule then we must have its criteriaaa, i got it

[ancient lava]

yep

ok now this one

4m^2

[shell pendant]

(2)^2m

?

Why dont we use this "²" instead of "^"?

[ancient lava]

oh

well idk how to write it here that’s why

[shell pendant]

Oh okay i understand

[ancient lava]

^2 means the same thing you mentioned

[shell pendant]

yes

[ancient lava]

4m^2

this is how you should think about it

4 is a square number

m is also squared there

so we can write them both together as (2m)^2

now what about 9m^2

[shell pendant]

(3m)^2?

[ancient lava]

yes!

What about this one

[shell pendant]

yay!

[ancient lava]

16x^2

[shell pendant]

(2x)^4?

Is this allowed

Or am i supposed to use ^2 only?

[ancient lava]

yes it is, only if x^4

but here just try to use ^2

[shell pendant]

Oh okay

[ancient lava]

because we are trying to use a^2 - b^2

[shell pendant]

Okay2

(4x)^2

😄

[ancient lava]

yep!

now let’s actually use it

[shell pendant]

okay

[ancient lava]

16x^2 - 1

[shell pendant]

how do I turn negative 1 into something like b²?

[ancient lava]

Don’t turn -1 into b^2

We are just talking about 1

not the negative sign

a^2 - b^2

[shell pendant]

(4x)²-1
(a-b)(a+b)
(4x-1) (4x+1)

[ancient lava]

YEESSS!

[shell pendant]

im forgetting how to use it little by little now

[ancient lava]

that is correct

[shell pendant]

Wow

[ancient lava]

lol no worries, just look at formulas before the exam

[shell pendant]

Thank youuuu

[ancient lava]

No problem

[shell pendant]

Yeah i definietly will do that

[ancient lava]

you gotta sleep

[shell pendant]

I do have to

[ancient lava]

ok not to be annoying, just this last example and we are done

[shell pendant]

Alright go for it

[ancient lava]

because you are probably on your bed and can’t write anything

[shell pendant]

Im still on my table mate

[ancient lava]

just tell me what things can be canceled out

[ancient lava]

Ah lol

ok

You don’t have to spend a lot of time

just show me what you got

[shell pendant]

I wrote the calculation on my paper

So fat i got this

Far*

[ancient lava]

Yes xD

[shell pendant]

5(x+2)/6z² x 3z/(x-2y)(x+2y)

I took long time to remember what i learnt and had to scroll my gallery to find the important things u sent

[ancient lava]

you have learnt it so well!

[shell pendant]

youre good teacher and thank you

I gotta arrange books in my bag for tommorrows classes

Ill seek out for help when I need

[ancient lava]

Ah ok

[shell pendant]

Youre very helpful.

[ancient lava]

One thing before you go

[shell pendant]

What?

[ancient lava]

What I didn’t tell you was that the question I just gave you, is the same thing you asked here

And you did it!

alright hope you will do the best on your exam!

[shell pendant]

What the heck

what is this plot twist

WOWWW THANK YOU

[ancient lava]

you are welcome!

[shell pendant]

THATS CRAZY

May you have a good life

Im gonna do what I gotta do now

[ancient lava]

Thanks

[shell pendant]

Thank you a LOT

[ancient lava]

And thank you for being here and actually paying attention to what I told you

cya later!

And good night

[shell pendant]

Cya!

to you too

.solved