help-0

[oak chasm]

Right.

[shy oasis]

oh ok

[oak chasm]

So, we bring it to the top like that.

[shy oasis]

so now its 3x^3y^-2

[ocean seal]

Chai T. Rex

[oak chasm]

The one on top is still there.

[shy oasis]

oh so we bring two y's?

up

[oak chasm]

No, we erase the y power on the bottom.

We switch the sign of the exponent.

[shy oasis]

so bascially its just one y

[oak chasm]

We write it on top with all the stuff that was already there.

No.

[shy oasis]

oh ok

[oak chasm]

3x³y was already there.

We're including y⁻² in that.

[shy oasis]

ahh gotcha

[oak chasm]

So, we write what we had and we write what we're including.

So, we have yy⁻².

So, we add the exponents.

What exponent do you get?

[somber osprey]

imposter sus

[shy oasis]

6?

which exponents

yy⁻².

[unborn dome]

can someone help me out on this?

wait is this channel busy...

[oak chasm]

@unborn dome Sorry, channel is busy.

What's the exponent on the first y?

[shy oasis]

-2?

[oak chasm]

No, the y on the left.

[shy oasis]

3..

[oak chasm]

No, that's the x.

[shy oasis]

im realy not sure

[oak chasm]

OK, what is on the top?

[shy oasis]

3x^3yy^-2

[oak chasm]

Look at the first y.

What is its exponent?

[shy oasis]

i really dont know

y?

i only see y

[oak chasm]

OK, so if something doesn't have an exponent, the exponent is 1.

[shy oasis]

im so dumb

[hot island]

Ohh

Yeah

I remember now

X = 1

Y = 1

[oak chasm]

@hot island Please stop interrupting.

[hot island]

I'm not interrupting

Geez just listening in

Didn't know this was a touchy subject

[shy oasis]

so if theres no number next to the letter it means its 1

@hot island u can listen but not type

[oak chasm]

@shy oasis Yes, the first power means you have one copy of the thing.

And we have one copy of y.

[shy oasis]

yes so now we get y^-3

[oak chasm]

No, we add the exponents.

What's 1 + -2?

[shy oasis]

1 + -2

3

[hot island]

2y-²

[oak chasm]

<@&268886789983436800> Repeated interruptions with incorrect information after repeatedly being asked to stop by both of us by @hot island

@shy oasis No.

[shy oasis]

-1

[oak chasm]

Right.

[shy oasis]

sorry i just get confushed when there is a negative number and theres a addition sign

[tame falcon]

@hot island Knock it off.

[hot island]

@oak chasm

[sly mantle]

muted

[shy oasis]

where were we

[oak chasm]

Thanks.

[shy oasis]

so we got -1

1 + -2

=1

-1*

[ocean seal]

Chai T. Rex

[shy oasis]

yes

[oak chasm]

So, now we have a negative exponent on top, so we can move it to the bottom.

How do we do that?

[shy oasis]

we make the -1 to a positive when we move it

4y^1

wait no

[oak chasm]

Right!

[shy oasis]

oh

[ocean seal]

Chai T. Rex

[shy oasis]

does the 3x^3 become 27x

[oak chasm]

Nope, remember that the exponent is like 3(x³).

It only applies to the thing right next to it.

[shy oasis]

so bascially it has invisible parenthese

right

[oak chasm]

Right.

That's also true with signs.

-x² is -(x²).

That's because the sign is like -1 times the number.

-1x² is -1(x²).

[shy oasis]

yea

[oak chasm]

So -x² is -(x²).

[shy oasis]

so what do i do for 3x^3 now

[oak chasm]

Oh, that's it.

You have each variable on only one side of the fraction.

You have no negative exponents.

And the nonvariable numbers are reduced.

3/4 is a simplified fraction.

[shy oasis]

oh so thats my answer?

[oak chasm]

Yes, that's right.

[shy oasis]

ahh ok

is it ok if i ask u a couple more questions if u have the time

[oak chasm]

Sure.

[shy oasis]

ur a really good helper

[oak chasm]

I have to go in about an hour.

Thanks.

[shy oasis]

ok

simplify a radical expression involving variables.

[ocean seal]

Chai T. Rex

[shy oasis]

i think so

[oak chasm]

OK, what do you get?

[shy oasis]

2/7

[ocean seal]

Chai T. Rex

[oak chasm]

OK, now we have x² under the square root, too.

[ocean seal]

Chai T. Rex

[oak chasm]

You know about absolute value?

[shy oasis]

i do but i forgot

[oak chasm]

It converts negative numbers to their positive version and leaves other numbers alone.

|-3| = 3, |0| = 0, and |3| = 3.

[shy oasis]

but we dont have to because its already a positive

[oak chasm]

No, x can be any number.

x = -3 has x negative.

[shy oasis]

how is x a negative

[oak chasm]

Because it's equal to -3 in that example.

And -3 is negative.

[shy oasis]

so now its -3^2

im kinda confused of the -3 part of how u got it

[oak chasm]

That's an example I gave, not what x is in your problem.

[shy oasis]

oh ok

[oak chasm]

If x = -3, then x is negative.

[shy oasis]

yes

[oak chasm]

Also, if x = -3, then -x is positive.

[shy oasis]

yea

[oak chasm]

OK, so back to the problem.

[ocean seal]

Chai T. Rex

[oak chasm]

Let's go over why that is.

Let's say x = -3.

[ocean seal]

Chai T. Rex

[oak chasm]

What do we do first to get the result of that?

[shy oasis]

not really sure

[oak chasm]

Well, inside the square root, we have just one thing to do.

The exponent.

What's (-3)²?

[shy oasis]

ahh so we multiply it

wait no

wait yea

which is 9

3 becomes a positive

[ocean seal]

Chai T. Rex

[oak chasm]

What's the square root of 9?

[shy oasis]

3

[oak chasm]

Right, so it's like taking the absolute value.

The -3 became a 3.

[shy oasis]

ohhh

[ocean seal]

Chai T. Rex

[shy oasis]

so now its just 2/7x

or thats wrong

[ocean seal]

Chai T. Rex

[oak chasm]

Do you see how we got that?

[shy oasis]

yeea

because we multpliyed x twice

x^2 but we still got x

[oak chasm]

No, it's because of what we just learned.

If you have x² under the square root, you take it out of the square root as |x|.

[shy oasis]

oh ok

[oak chasm]

And if you have 28 under the square root, 2 comes out and 7 stays in.

So, the 2 and the |x| are outside.

7 is left inside.

[ocean seal]

Chai T. Rex

[shy oasis]

ok

whats next

[oak chasm]

Oh, that's it.

[shy oasis]

ohg

[oak chasm]

You can't do anything else with the stuff under the square root.

[shy oasis]

sorry if its blurry

[candid thistle]

x is an angle, the line with length 10 is an angle bisector. How can I find r and s (preferably without trig cuz I don't understand it)

[oak chasm]

@candid thistle Sorry, channel is busy.

[candid thistle]

Remember that $\sqrt[a]{b} = b^{1/a}$

[ocean seal]

Eat water it's good

[candid thistle]

Okay, lemme ask somewhere else

[oak chasm]

@shy oasis This is correct ^

[ocean seal]

Chai T. Rex

[shy oasis]

yes

[candid thistle]

Which is also equal to ...

[ocean seal]

Chai T. Rex

[candid thistle]

Now simplify :)

[oak chasm]

Do you see why they're equal?

[shy oasis]

yea

[oak chasm]

OK, now we do what we learned a while back.

[candid thistle]

simplify!

[oak chasm]

You have two things multiplied in the parentheses.

So, you take each of them to the power outside of the parentheses.

[candid thistle]

$(ab)^c = \text{what?}$

[ocean seal]

Eat water it's good

[shy oasis]

so now i take 15 out>

[candid thistle]

No because the 15 is not on the 8

take the 1/3 in

(ig)

[shy oasis]

im not sure what to take out

[oak chasm]

OK, so you don't take anything out.

[shy oasis]

yea

[oak chasm]

What you do is you have two things multiplied together in parentheses all to a power.

[shy oasis]

yes

[ocean seal]

Chai T. Rex

Chai T. Rex

[shy oasis]

do we do 8x^1/3?

[oak chasm]

Nope.

[oak chasm]

See this ^

[shy oasis]

yes

[oak chasm]

So, what's a in our problem?

[shy oasis]

8

[oak chasm]

What's b?

[shy oasis]

15

[oak chasm]

Nope.

[shy oasis]

x

[oak chasm]

What are we multiplying with 8?

[shy oasis]

1/3

[oak chasm]

Nope.

[ocean seal]

Chai T. Rex

[shy oasis]

im not sure what b is

[oak chasm]

b is inside the parentheses, right?

[shy oasis]

correct

oh

[oak chasm]

1/3 is outside.

[candid thistle]

there are two terms inside the parentheses, these are-

[shy oasis]

x^15

[oak chasm]

Right.

a = 8

b = x¹⁵.

What's c?

[shy oasis]

yes

1/3

c=1/3

[oak chasm]

Good.

[candid thistle]

$(8 \cdot x^{15})^{1/3}$

[ocean seal]

Eat water it's good

Chai T. Rex

[oak chasm]

Fill in a, b, and c on the right part.

What do you get?

[shy oasis]

(8)^1/3

[candid thistle]

Ooh so if you have (\text{test}) then it is a light background, otherwise $\text{test}$ gives a dark background?

[shy oasis]

(x^15)^1/3

[candid thistle]

And simplify-

[shy oasis]

sorry im getting confused cuz theres two people typing at once

[candid thistle]

Sorry, I will stop

[shy oasis]

ty

2

for a and c

[oak chasm]

In a private message with @ocean seal, say ,texconfig color help

@shy oasis OK, now put them next to each other.

[shy oasis]

x^5

i got 2 and x^5

[ocean seal]

Chai T. Rex

[oak chasm]

Right, so the answer is 2x⁵.

[shy oasis]

thats it?

ok one more before you go

last one

[oak chasm]

Yes, the power on the outside goes to each factor on the inside.

OK.

[ocean seal]

Chai T. Rex

[shy oasis]

3/4

[oak chasm]

Nope.

[shy oasis]

2/3

wait why is it 2/3 again

[oak chasm]

Because 2² = 4.

Well, let's do it this way.

Factor 12 into prime powers. What do you get?

[shy oasis]

idk

[oak chasm]

OK, what are the first few primes?

[shy oasis]

2,3,5,7

[oak chasm]

OK, is 2 in 12?

[shy oasis]

yes

[oak chasm]

OK, divide 12 by 2 then.

What do you get?

[shy oasis]

6

[oak chasm]

Is 2 in 6?

[shy oasis]

yes

[oak chasm]

OK, divide 6 by 2.

What do you get?

[shy oasis]

3

[oak chasm]

Is 2 in 3?

[shy oasis]

no

[oak chasm]

OK, go to the next prime, 3.

Is 3 in 3?

[shy oasis]

yes?

[oak chasm]

OK, divide 3 by 3.

[shy oasis]

1

[oak chasm]

And with 1, we stop.

So, what did we divide by?

2, 2, and 3, right?

[shy oasis]

correct

[oak chasm]

OK, now square root is the second root, right?

[shy oasis]

yes

[oak chasm]

So the primes have to leave in matching groups of two of the same prime.

Two because it's the second root.

If it was a cube root, the third root, we'd need groups of three of the same prime.

If it was the 100th root, we'd need groups of 100 of the same prime.

Does that make sense?

[shy oasis]

yea

[oak chasm]

OK, so let's look at each prime.

We have 2 as one of them.

[shy oasis]

so like it has to be the same number

[oak chasm]

Is there a group of two of the prime 2?

[shy oasis]

like 2 2

[oak chasm]

Right.

[shy oasis]

100 and 100

[oak chasm]

Or 7 7

[shy oasis]

got it

which stops at 1

and cant go further

[oak chasm]

What stops at 1?

[shy oasis]

wait nvm

[oak chasm]

That was for getting the prime factorization.

This is a different step after that's done.

Now we have the primes, 2, 2, and 3.

It's the second root, so we need groups of two of the same prime.

Do we have any groups of two of the same prime?

[shy oasis]

2 2

[oak chasm]

Good, so that's one group of 2s.

That group left the square root.

We have 3 as the primes left over.

Do we have any groups of two of the same prime?

[shy oasis]

no

[oak chasm]

OK, so one group of 2 left. 3 couldn't get out.

[ocean seal]

Chai T. Rex

[oak chasm]

Let's try it with 48.

[ocean seal]

Chai T. Rex

[oak chasm]

What are the primes in 48?

[shy oasis]

2

48 divided by 2 is 24

[oak chasm]

Good, go on.

[shy oasis]

24 divided by 2 is 12

12 divided by 2 is 6

6 divided by 2 is 3

ohhh i see the pattern now

[oak chasm]

OK, so, 2, 2, 2, 2, 3.

How many groups of two 2s are there?

[shy oasis]

4

[oak chasm]

Nope.

That's how many 2s, not how many groups of two 2s.

[shy oasis]

2 groups

[oak chasm]

Right.

How many groups of two 3s are there?

[shy oasis]

1

[oak chasm]

Nope.

[shy oasis]

none

[oak chasm]

Right.

So, all the groups left.

How many 2s are left?

[shy oasis]

1

[oak chasm]

No.

[shy oasis]

none

[oak chasm]

Right.

How many 3s are left?

[shy oasis]

1

[oak chasm]

Right.

[shy oasis]

its just 3 now

[ocean seal]

Chai T. Rex

[oak chasm]

Two groups of 2 made it out.

One 3 is stuck.

Does that make sense?

[shy oasis]

is this part of the problem?

[oak chasm]

No, this is so you know how to simplify square roots of integers.

[shy oasis]

it makes sense

[oak chasm]

OK, so let's go back to the problem.

[ocean seal]

Chai T. Rex

Chai T. Rex

Chai T. Rex

[oak chasm]

We have nine xs, right?

[shy oasis]

yea

IxI

[oak chasm]

OK, so how many groups of two xs are there?

[shy oasis]

4

[oak chasm]

How many are left over?

[shy oasis]

1

[ocean seal]

Chai T. Rex

[oak chasm]

Does that make sense?

[shy oasis]

yea

[oak chasm]

OK, can x⁴ be negative?

[shy oasis]

cuz theres 4 groups of x and the one x geets left behind

inside

[oak chasm]

Yes, that's right.

And since it's a variable, it gets an absolute value in case it's negative.

Now, can x⁴ be negative?

[shy oasis]

no

[oak chasm]

OK, so the absolute value won't change what's inside since it's not negative.

It does nothing.

[ocean seal]

Chai T. Rex

[shy oasis]

ok

[oak chasm]

So, let's combine everything.

[ocean seal]

Chai T. Rex

[oak chasm]

We combine the parts in the square roots.

[ocean seal]

Chai T. Rex

[oak chasm]

We combine the 3 and 2. We combine the x powers.

[ocean seal]

Chai T. Rex

[oak chasm]

See how that works?

Or any questions?

[shy oasis]

yea

cuz u multiplied 3x2

and added 2+4

[oak chasm]

Good.

[shy oasis]

you should be a teacher

ur really good at this

[oak chasm]

Thanks.

[shy oasis]

ill give u a follow on twitch

i sent you a friend request

[oak chasm]

Oh, I'm not really on Twitch (at least as a streamer).

[shy oasis]

do u like mod?

[oak chasm]

What's mod?

[shy oasis]

its someone who helps keep weirdos out of chat

[oak chasm]

Oh!

[shy oasis]

bascially perms to ban people

[oak chasm]

Yeah, they help keep things running smoothly.

[shy oasis]

or time them out

yup!

[hollow pelican]

how to remove log on both sides?

[shy oasis]

ok so that was the answer?

[oak chasm]

Yes, that's right.

Did you have any other questions?

[shy oasis]

do u know how to graph?

[oak chasm]

Yes.

@hollow pelican Sorry, channel is busy.

[hollow pelican]

ok

[shy oasis]

sorry if im asking for help too much

[oak chasm]

#help-9 looks open.

No, that's fine

[shy oasis]

i want to make sure i get a good grade for my quiz

and study them

1b

[oak chasm]

OK, so that's in standard form.

[shy oasis]

yes

[oak chasm]

The trick with graphing that is that you can find the x and y intercepts.

Do you know how?

[shy oasis]

yes

[oak chasm]

OK, what are the intercepts?

[shy oasis]

x, y?

[oak chasm]

Yes, what is the x intercept?

[shy oasis]

2

and y is 3

[oak chasm]

Nope.

[shy oasis]

oh

[oak chasm]

Here's how you do it.

y intercept is on the y axis.

The y axis is where x = 0.

Like if you look at the points on the y axis, you have things like (0, 1).

That's 1 up from the origin.

That's on the y axis.

You have things like (0, -10000).

That's 10000 down from the origin.

That's on the y axis.

Does that make sense?

[shy oasis]

yea

i know that

y goes up and down

[oak chasm]

OK, so x = 0 on the y axis. The y intercept is on the y axis.

So for the y intercept, x = 0.

3x + 2y = -6.

Fill in x with (0).

Because x = 0.

3(0) + 2y = -6.

[shy oasis]

its 2x+3y=-6

[oak chasm]

0 + 2y = -6

Oh, sorry.

2x + 3y = -6

2(0) + 3y = -6

0 + 3y = -6

3y = -6

See how the x term disappeared?

[shy oasis]

i know how

its because u added 2 to 2x and -6

[oak chasm]

I didn't add anything.

[shy oasis]

oh ok

[oak chasm]

x = 0 on the y axis, right?

[shy oasis]

yes

[oak chasm]

The y intercept is on the y axis, right?

[shy oasis]

yes

[oak chasm]

OK, so the y intercept will have x = 0 since it's on the y axis.

2x + 3y = -6

2(0) + 3y = -6

Do you see how I filled in x with (0)?

[shy oasis]

yea

[oak chasm]

0 + 3y = -6

3y = -6

Do you see how the x term disappears?

[shy oasis]

yea

sorry my teacher taught me it differently to get 0

[oak chasm]

OK, so to get one of the intercepts, you erase the other variable's term.

2x + 3y = -6

y intercept, so erase x term

3y = -6

2x + 3y = -6

[shy oasis]

now i do -6 divided by 3

[oak chasm]

x intercept, so erase y term

2x = -6

With standard form, to find an intercept erase the term with the other variable and solve.

[shy oasis]

yea

[oak chasm]

So, what's the y intercept?

[shy oasis]

3

[oak chasm]

Nope.

[shy oasis]

-3

[oak chasm]

Nope.

[shy oasis]

-2

[oak chasm]

What's the equation?

[shy oasis]

-6 divided by 3\

[oak chasm]

Right.

So, -2.

[shy oasis]

2

-2

[oak chasm]

OK, what's the x intercept?

[shy oasis]

-3

[oak chasm]

Right.

So, mark the y intercept at (0, -2).

Mark the x intercept at (-3, 0).

Tell me when you've marked those points.

[shy oasis]

wait so its just a straight line then

[oak chasm]

Yes, connect those points with a straight line.

And also draw the line all the way to the edges of the graph.

[shy oasis]

is it suppose to be like this?

wait i made a mistake

[oak chasm]

The y intercept is on the y axis.

The x intercept is on the x axis.

You have them both on the y axis.

[oak chasm]

That's probably close enough.

Better to do it with a ruler, but if you don't have a ruler, you can do it this way.

[tight haven]

Hello

[oak chasm]

@tight haven Sorry, channel is busy.

[tight haven]

Got it

[oak chasm]

So, going from the y intercept to the x intercept, you go up 2 and left 3, right?

[shy oasis]

yes

correct

[oak chasm]

OK, so from there, go up 2, left 3 again and mark that point.

Then, from there, go up 2, left 3 again and mark that point.

And so on until you can't.

[shy oasis]

wait i got it right right?

[oak chasm]

No, it's slightly off.

Did you mark those points?

[shy oasis]

yea

[oak chasm]

OK, now go back to the y intercept.

[shy oasis]

its on (-3,0)

[oak chasm]

What's on (-3, 0)?

[shy oasis]

x intercept

[oak chasm]

OK, start at the y intercept.

You have to go up 2 and left 3 to get to the x intercept, right?

[shy oasis]

yea thats what i did

[oak chasm]

OK.

So, you marked that point at the x intercept.

Now start at the x intercept.

[shy oasis]

yes

[oak chasm]

Go up 2 and left 3 from there.

You're at a point you haven't marked yet, right?

[shy oasis]

im getting confused

i marked (-3,0) and (0,-2)

[oak chasm]

Yes.

And did you mark the third point?

[shy oasis]

no yet

sorry my wifi turned off

where where we

not yet*

[oak chasm]

OK, to get from the y intercept to the x intercept, you go up 2 and left 3, right?

[shy oasis]

yes

[oak chasm]

OK, now start at the x intercept.

Not the y intercept.

[shy oasis]

ok

[oak chasm]

The x intercept.

Go up 2, left 3 from there.

That's a point you haven't marked yet, right?

[shy oasis]

i marked it already

[oak chasm]

OK. From that point, go up 2, left 3.

Mark that point.

How many points have you marked?

[shy oasis]

marked the third point

i got it

[oak chasm]

OK, now mark the fourth point.

Then, keep going. When you reach the end of the graph,

Start at the y intercept again.

[shy oasis]

done

[oak chasm]

Go down 2, right 3.

Mark the point.

Keep going down 2, right 3 until you reach the end of the graph.

[shy oasis]

i thought u said go up and left 3

[oak chasm]

OK, what point did you mark last?

[shy oasis]

the third one

[oak chasm]

Did you mark a fourth one?

[shy oasis]

yea

u said to go up 2 and left 3

[oak chasm]

OK, the last point you marked is the fourth point.

[shy oasis]

yea

its at the very end of the line

[oak chasm]

So, how do you get from the fourth point to the third point?

[shy oasis]

2 up and left 3

[oak chasm]

No.

Look at the actual fourth point.

Look at the actual third point.

How do you get from the fourth point to the third point?

[shy oasis]

im not sure

[oak chasm]

Do you go up or down?

[shy oasis]

up

[oak chasm]

No.

[shy oasis]

was i suppose to go down

from the third point?

[oak chasm]

I didn't say from the third point.

[shy oasis]

x

[oak chasm]

I asked how do you get from the fourth point to the third point.

In that question, what point do you start at?

[shy oasis]

third point

[oak chasm]

No.

If I ask you how to get from New York to San Diego, what city do you start in?

[shy oasis]

new york

[oak chasm]

If I ask you how to get from the fourth point to the third point, what point do you start at?

[shy oasis]

oh i went 3 right and 2 down

from fourth point to third

[oak chasm]

Nope.

[shy oasis]

right*

[oak chasm]

Right.

Do you see how the points are neighbors to both the point 2 up and 3 left and the point 2 down and 3 right?

[shy oasis]

yea

[oak chasm]

OK, so start at the y intercept.

Go 2 down and 3 right. Mark the point.

Go 2 down and 3 right. Mark the point.

And so forth.

[cerulean vine]

sorry if im interrupting but i came across these Singaporean Isometric questions and i dont quite understand em

[oak chasm]

@cerulean vine Sorry, channel is busy.

[shy oasis]

so i keep doing the same thing

[cerulean vine]

oh k

[oak chasm]

#help-5 looks open.

[shy oasis]

so i keep going?

[oak chasm]

Yes until you go off the graph.

[shy oasis]

like this?

[oak chasm]

Yes, now those are guidepoints.

Make sure the line goes through them.

[errant jolt]

Express
−𝟏𝟐𝟓
𝟔𝟒
as an exponent
answer

[shy oasis]

ok

[oak chasm]

@errant jolt Sorry, channel is busy.

@shy oasis So, basically you find out how to get from one intercept to another.

You keep moving like that until you go off the groph.

[shy oasis]

so i got it right?

[oak chasm]

Then you go back to the start and go the other direction.

Yes, except the line on the far right doesn't exactly go through the last point.

[shy oasis]

yea this is for practice

[oak chasm]

Oh, OK.

[shy oasis]

im gonna use a ruler for the quiz

lol\

[oak chasm]

Oh, good.

[shy oasis]

what about 1d

[oak chasm]

OK, so standard form has the variables on the left and the constant on the right.

So, move the constant to the right.

[shy oasis]

not sure how to do that

[oak chasm]

Do you know how to move a term to the other side of an equation?

[shy oasis]

i kinda forgot

[oak chasm]

x - 6 = 0

How do you move the -6 to the other side?

[shy oasis]

0 = x - 6?

[oak chasm]

No.

Just the -6, not anything else.

[shy oasis]

oh ok

so x-0=6

wait thats wrong

x0=-6

[oak chasm]

No.

[shy oasis]

im not really sure

[oak chasm]

What do you do to both sides?

[cerulean vine]

is this channel free?

[shy oasis]

add?

idk

[cerulean vine]

nvm

[oak chasm]

Right!

x - 6, right

[shy oasis]

yes

x= -6

[oak chasm]

It's connected to the rest by subtraction.

The opposite of subtraction is addition.

Add 6 to both sides.

Does that make sense?

[shy oasis]

x=0

[oak chasm]

No, hold on.

Does that make sense?

[shy oasis]

kind of

[oak chasm]

OK, let's look at just the left side.

x - 6

How is 6 connected to the rest?

[shy oasis]

because of 3y?

i think

[oak chasm]

Sorry?

There was no 3y in x - 6.

[oak chasm]

Right.

I asked you to move 6 to the right side in x - 6 = 0, right?

[shy oasis]

oh yea

[oak chasm]

OK, let's look at the left side.

x - 6

How is 6 connected to the rest?

[shy oasis]

1/2x-6 right?

[oak chasm]

No.

x - 6 = 0.

[shy oasis]

im not really sure

[oak chasm]

What's happening with x - 6?

What is done in it?

[shy oasis]

sorry which from is this again

[oak chasm]

Sorry?

[shy oasis]

form*'

[oak chasm]

That doesn't matter.

What does x - 6 mean?

[shy oasis]

1

[oak chasm]

No.

[shy oasis]

what do you mean by x-6

thats the park confusing me

[oak chasm]

Have you done algebra before?

[shy oasis]

part*

yea

[oak chasm]

What does x - 6 mean in algebra?

[shy oasis]

but i kinda forgot

[oak chasm]

What does x mean?

[shy oasis]

1

[oak chasm]

No.

What does x mean?

[shy oasis]

idk

[oak chasm]

It's a variable.

It stands for a number.

Do you remember that from learning algebra?

[shy oasis]

from 7th grade yea

idk the number it stands for

[oak chasm]

I didn't ask what number it equals.

I asked what it was.

What does it mean?

It's a variable.

[shy oasis]

yes

[oak chasm]

It stands for a number.

What does - mean?

[shy oasis]

unknown number?

[oak chasm]

No.

[shy oasis]

i really dont know what it means

[oak chasm]

Do you remember what - means from grade school?

Have you seen a subtraction problem before?

[shy oasis]

yes

[oak chasm]

What does - miean?

[shy oasis]

u mean median?

[oak chasm]

Noo, we're not doing statistics.

Do you remember doing subtraction before?

[shy oasis]

i do

[oak chasm]

What does the - in a subtraction problem mean?

[shy oasis]

minus sign

[oak chasm]

That's what it is.

What does it mean?

[shy oasis]

minus sign

[oak chasm]

No.

That's what it is, not what it means.

What does it mean?

[shy oasis]

subtract

[oak chasm]

Subtract what from what?

[shy oasis]

x from 6

[oak chasm]

No., 6 from x.

[shy oasis]

oh yea

6 from x

[oak chasm]

So, x - 6 means to subtract 6 from x.

[shy oasis]

yes

[oak chasm]

How is 6 connected to the rest of x - 6?

[shy oasis]

not sure

[oak chasm]

It's being subtracted from it.

[shy oasis]

i was gonna say that but i wasnt sure

ok

what do i do next

[oak chasm]

What's the opposite of being subtracted from something?

[shy oasis]

adding

[oak chasm]

Being added to it.

[shy oasis]

yes

[oak chasm]

So, we add 6 to it.

x - 6 + 6

What does that simplify to?

[shy oasis]

x

[oak chasm]

Do you see how it's not on that side now?

[shy oasis]

yea

[oak chasm]

OK, so we need to do the same thing to both sides.

x - 6 = 0

We add 6 to both sides.

x - 6 + 6 = 0 + 6

What does that simplify to?

[shy oasis]

x=6

[oak chasm]

OK, so that's how you move a term to the other side.

[shy oasis]

ok

[oak chasm]

So, let's go back to the problem.

[shy oasis]

ok

[oak chasm]

1/2 x + 3y - 6 = 0

How can we get the 6 to the other side?

[shy oasis]

add 6 to both sides

[oak chasm]

OK, what do you get when you do that?

[shy oasis]

do we add 6 to -6 and 0?

[oak chasm]

No, you add 6 to both sides.

[shy oasis]

to what

[oak chasm]

To the left side and to the right side.

[shy oasis]

im talking about what numbers

do i need to add 6 to

[oak chasm]

Everything on the left side.

Everything on the right side.

[errant jolt]

13.045 x 𝟏𝟎 ^ 5 expanded form

Answer

[oak chasm]

@errant jolt Sorry, channel is busy.

[errant jolt]

Could you please help me

[shy oasis]

like that

[oak chasm]

Not each thing, everything together.

(1/2 x + 3y - 6) + 6 = (0) + 6

[shy oasis]

oh that?

so i add like (1/2 x + 3y - 6) + 6 = (0) + 6

[oak chasm]

Yes.

You add 6 to both sides.

It has the left side plus 6.

It has the right side plus 6.

[shy oasis]

x=-6y+12

[oak chasm]

No, you've gone too far.

Simplify just what I said.

What do you get?

[shy oasis]

im not sure how to simplify on the left

i got 6 from (0) +6

[oak chasm]

OK, so addition is the last thing in PEMDAS.

So, you don't need the parentheses.

[shy oasis]

ok

[oak chasm]

This is because doing the stuff in parentheses first and then doing the addition is the same thing as without parentheses.

You're going to do everything that used to be in parentheses first anyway.

[shy oasis]

i have to turn this in at 11:59

by

[oak chasm]

OK, so simplify the left side.

[shy oasis]

how do i do it

im really sure

so its 1/2x +3y -6 +6 correct?

[oak chasm]

Yes.

Now combine like terms.

[shy oasis]

x/2 + 3y

[oak chasm]

OK.

So, 1/2 x + 3y = 6

Now what does standard form look like?

[shy oasis]

yes

it does

[oak chasm]

ax + by = c

Wher a, b, and c are integers that don't all have a common factor.

1/2 isn't an integer.

[shy oasis]

2

[oak chasm]

So, multiplying it by 2 will work.

But you can't just multiply part of it by 2.

You have to multiply both sides by 2.

[shy oasis]

are we allowed to go the mathematics vc

[oak chasm]

I don't have a microphone.

[shy oasis]

oh ok

[oak chasm]

But you see how 1/2 can be changed to an integer by doubling it?

[shy oasis]

wydm by doubling it

like adding it?

[oak chasm]

Doubling means multiplying by 2.

@main zephyr Sorry, this channel is busy.

[main zephyr]

oh alright

[shy oasis]

so 1/2 x 2?

[odd minnow]

Im the cia

[oak chasm]

Yes, but with an equation, you can't just multiply one part of it by 2.

You have to do the same thing to both sides.

So, multiply both sides by 2.

[pastel panther]

hi guys

[oak chasm]

2(1/2 x + 3y) = 2(6)

[shy oasis]

so what does that turn out

[oak chasm]

@pastel panther Sorry, channel is busy.

[shy oasis]

=12

[oak chasm]

What about the left side?

[shy oasis]

im struggling on how to multiply the left side tbh

can u teach me

[oak chasm]

Do you know the distributive property?

[shy oasis]

yes

but i forgot

[oak chasm]

a(b + c) = ab + ac

[shy oasis]

what do i do next

[oak chasm]

Do you see how the distributive property works?

[shy oasis]

yea

[oak chasm]

OK, how does it work?

[shy oasis]

i multply 2 to 1/2 and 3

[oak chasm]

Well, almost.

You multiply 2 by 1/2 x and by 3y.

Then you add those together.

[shy oasis]

7

1 + 6

[oak chasm]

No.

You don't multiply 2 to 1/2 and 3.

Like I said, you multiply 2 by 1/2 x and 3y.

[shy oasis]

so 1/2 by 2?

[oak chasm]

No.

2 times 1/2 x

[shy oasis]

x

[oak chasm]

Right.

Now 2 times 3y.

[shy oasis]

6

[oak chasm]

No.

[shy oasis]

idk

[oak chasm]

That's 2 times 3.

We're not multiplying 2 times 3.

We're multiplying 2 times 3y.

[shy oasis]

6y

[oak chasm]

Yes.

Now add them together.

[shy oasis]

7y

[oak chasm]

No.

What are the two terms?

[shy oasis]

x+ 6y

[oak chasm]

Yes.

x + 6y = 12

[shy oasis]

yes

[oak chasm]

Now it's in standard form.

[shy oasis]

yup

[oak chasm]

Now you can find the x and y intercepts.

But let's recap.

1/2 x + 3y - 6 = 0

That's what we started with.

That's not in standard form.

[shy oasis]

yes

correct

[oak chasm]

We have the variables on the left and the constant on the right in standard form.

So, we moved the constant to the right side.

[shy oasis]

mhm

yes

[oak chasm]

Then we fixed everything to have integer coefficients.

Then it was in standard form.

So now, what are the intercepts?

[shy oasis]

x=6

[oak chasm]

No.

x + 6y = 12

[shy oasis]

ok

[oak chasm]

What is y at the x intercept?

[shy oasis]

0

[oak chasm]

Fill in (0) for y.

[shy oasis]

so its (6,0)

[oak chasm]

No.

Fill in (0) for y.

[shy oasis]

im not getting you

[oak chasm]

x + 6y = 12

Fill in (0) for y.

[shy oasis]

x+6(0)=12

[oak chasm]

Right.

Simplify.

[shy oasis]

i geet 6

[oak chasm]

That's not a simplified equation.

I didn't ask you to solve it.

I said to simplify it.

[golden basalt]

Can someone help

[oak chasm]

@golden basalt Sorry, channel is busy.

[golden basalt]

Ok

[shy oasis]

12/6

[oak chasm]

That's not an equation.

That doesn't have an equal sign.

So it can't be a simplified equation.

I didn't ask for you to solve for x.

I said to simplify it.

[shy oasis]

x=6

[oak chasm]

No.

[shy oasis]

im not sure

[oak chasm]

Look at each term.

x

Is x simplified?

[shy oasis]

yes?

[oak chasm]

6(0)

Is 6(0) simplified?

[shy oasis]

no

[oak chasm]

Simplify it.

[shy oasis]

0

[oak chasm]

12

Is 12 simplified?

[shy oasis]

yes

no

[oak chasm]

x + 0 = 12

What can be simplified there?

[shy oasis]

12

[oak chasm]

How?

[shy oasis]

x

[oak chasm]

What?

You said 12 can be simplified.

I asked how, which means to give me a way it can be simplified.

x is not a way it can be simplified.

[shy oasis]

12/0?

[oak chasm]

What's that evaluate to?

[shy oasis]

12

[oak chasm]

No.

[shy oasis]

0

[oak chasm]

What can you multiply by 0 to get 12?

[shy oasis]

nothing

[oak chasm]

Then 12/0 isn't a number.

[shy oasis]

yes

[royal anvil]

hey guys im new here andi have a doubt

[oak chasm]

@royal anvil Sorry, channel is busy.

[royal anvil]

k

where should i ask my ques?