How do I solve equations? | Mathematics | Page 1

proud matrixBOT Jan 21, 2025, 10:24 PM

#

Do not ping the Moderators, unless someone is breaking the rules.
Do not ping the Helper Moderators, unless there is a conflict between helpers.
Do not ping other members randomly for help.
Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
Wait patiently for a helper to come along.
If the Helper has answered your question, remember to thank them with the Mathematics Ranks bot and close the thread with:

+close
Feel free to nominate the person for helper of the week in #helper-nominations
If you're happy with the help you got here, and the server overall, you can contribute financially as well:

rare spindle Jan 21, 2025, 10:28 PM

#

I don‘t know where to start

#

And I don‘t know why would you wanna solve an equation

vocal eagle Jan 21, 2025, 10:32 PM

#

Firstly what grade are you in

rare spindle Jan 21, 2025, 10:32 PM

#

7

vocal eagle Jan 21, 2025, 10:32 PM

#

Welp alright

#

Uh so when we're solving equations

#

What we want to do is isolate unknown terms on one side

#

And constants on the other side

rare spindle Jan 21, 2025, 10:33 PM

#

Okay

vocal eagle Jan 21, 2025, 10:33 PM

#

Sounds a bit abstract rn but I guess I'll give an example

#

Let's say we have 2x+3=x+2

#

Let's try to get x terms on the left and constants on the right

rare spindle Jan 21, 2025, 10:34 PM

#

So like 2x+x=3+2?

vocal eagle Jan 21, 2025, 10:34 PM

#

No not really

#

So firstly what we make use of

#

When we solve equations

#

Is whatever we do on the left side of the equation

#

Also happens on the right side

rare spindle Jan 21, 2025, 10:35 PM

#

Why tho?

vocal eagle Jan 21, 2025, 10:36 PM

#

We know that 5=5

rare spindle Jan 21, 2025, 10:36 PM

#

It wouldn‘t be the same equation then

vocal eagle Jan 21, 2025, 10:36 PM

#

Actually nvm bad example

#

Let's say you two people had the same amount of apples

#

And you stole the same number of apples from each of them

#

Would the two people still have the same amount of apples?

rare spindle Jan 21, 2025, 10:37 PM

#

Yes ig

#

And you can add apples as well, can‘t you?

vocal eagle Jan 21, 2025, 10:38 PM

#

When we use the = sign we're saying that both expressions on the left hand and right hand side of the equal sign are well equal

vocal eagle Jan 21, 2025, 10:38 PM

#

rare spindle And you can add apples as well, can‘t you?

Yea and they'd still be equal

#

If the same amt was added to each person

rare spindle Jan 21, 2025, 10:39 PM

#

Okay

#

Understood

vocal eagle Jan 21, 2025, 10:39 PM

#

So 2x+3=x+2

#

Let's subtract x from both sides

#

This brings x to the left hand side

rare spindle Jan 21, 2025, 10:39 PM

#

But we don‘t knoe what x is

vocal eagle Jan 21, 2025, 10:39 PM

#

This then becomes
x+3=2

vocal eagle Jan 21, 2025, 10:40 PM

#

rare spindle But we don‘t knoe what x is

Doesn't matter

rare spindle Jan 21, 2025, 10:40 PM

#

Oh okay

vocal eagle Jan 21, 2025, 10:40 PM

#

2x-x=x

#

Don't have to know what x is

rare spindle Jan 21, 2025, 10:40 PM

#

But can u just subtract both sides 2 so 2x becomes x?

vocal eagle Jan 21, 2025, 10:41 PM

#

That's what we're doing😭

#

This then becomes
x+3=2

#

From here can you finish the problem

static quarry Jan 21, 2025, 10:41 PM

#

Perhaps I might be able to help?

rare spindle Jan 21, 2025, 10:41 PM

#

Hi

static quarry Jan 21, 2025, 10:41 PM

#

Hi.

vocal eagle Jan 21, 2025, 10:42 PM

#

static quarry Perhaps I might be able to help?

Welp alright

rare spindle Jan 21, 2025, 10:42 PM

#

vocal eagle This then becomes x+3=2

Why 3+x=2

static quarry Jan 21, 2025, 10:42 PM

#

Okay, so here's the thing. What is an equation?

vocal eagle Jan 21, 2025, 10:42 PM

#

Just don't use too complex definitions please

rare spindle Jan 21, 2025, 10:42 PM

#

Wouldn‘t it be like 2x+3=x+2 and then subtract borh sides 2 so we get x+3=x and then minus x so 3=0

#

Oh wait

#

Ye nvm

#

Pls continue

static quarry Jan 21, 2025, 10:43 PM

#

rare spindle Pls continue

I mean, that was an actual question. What is an equation?

rare spindle Jan 21, 2025, 10:44 PM

#

static quarry I mean, that was an actual question. What is an equation?

Hmm

#

Find x?

#

That what our teacher told us

#

Find an x such that both sides are like same?

#

Are you guys still there?

vocal eagle Jan 21, 2025, 10:46 PM

#

static quarry I mean, that was an actual question. What is an equation?

I don't think Tony has a specific qn

#

The class is just on the topic of equations

static quarry Jan 21, 2025, 10:48 PM

#

rare spindle Hmm

The answer is that an equation is a statement.

#

It's an assertion that two expressions have equal value.

#

When we say, for instance, that 3x + 7 = 4 - 9x, we're saying that 3x + 7 and 4 - 9x are both numbers, and they're the same number.

rare spindle Jan 21, 2025, 10:50 PM

#

Numbers?

static quarry Jan 21, 2025, 10:50 PM

#

Yes.

rare spindle Jan 21, 2025, 10:50 PM

#

But there is an x

static quarry Jan 21, 2025, 10:50 PM

#

The x is a number.

rare spindle Jan 21, 2025, 10:50 PM

#

So it‘s a random number?

static quarry Jan 21, 2025, 10:50 PM

#

No.

rare spindle Jan 21, 2025, 10:51 PM

#

What are we trying to find?

#

X right

static quarry Jan 21, 2025, 10:51 PM

#

...yes...

rare spindle Jan 21, 2025, 10:51 PM

#

So if x is a number why is 4- 9x not a number

static quarry Jan 21, 2025, 10:52 PM

#

...it is a number. I said it was a number, you said it wasn't.

rare spindle Jan 21, 2025, 10:52 PM

#

Oh sorry my bas

static quarry Jan 21, 2025, 10:52 PM

#

Or expressed confusion.

rare spindle Jan 21, 2025, 10:52 PM

#

So you are tyring to find an x such that both sides have euqal value?

static quarry Jan 21, 2025, 10:53 PM

#

Right.

#

And the way that we do that is by transforming the equation.

rare spindle Jan 21, 2025, 10:54 PM

#

How do we transform it tho?

static quarry Jan 21, 2025, 10:54 PM

#

We make new equations that must be true if our starting equation is true.

#

For instance, if a = b, then a + c = b + c, right?

#

Where a, b, and c are all numbers.

rare spindle Jan 21, 2025, 10:55 PM

#

If two people have the same amount of apples and you give them 100 apples both they both still have the same amount?

#

Is it what u r trying to say?

static quarry Jan 21, 2025, 10:56 PM

#

...sure.

rare spindle Jan 21, 2025, 10:56 PM

#

Okok

static quarry Jan 21, 2025, 10:56 PM

#

Also, if a = b, then a - c = b - c.

#

And a * c = b * c.

#

And a / c = b / c (if c =/= 0).

rare spindle Jan 21, 2025, 10:57 PM

#

Hmm

#

One second I have ti write it down

#

Okay done

static quarry Jan 21, 2025, 11:00 PM

#

Okay, so.

#

Consider the equation 2x - 10 = 20 - x.

rare spindle Jan 21, 2025, 11:01 PM

#

-2x on both sides?

#

@vocal eagle said to seperate them

vocal eagle Jan 21, 2025, 11:02 PM

#

Well this is just the initial equation

#

And also don't ping me rn😭

rare spindle Jan 21, 2025, 11:03 PM

#

Okay my bad

static quarry Jan 21, 2025, 11:03 PM

#

rare spindle -2x on both sides?

Okay, so the ultimate goal is to get an equation that looks like x = c, where c is just some regular number.

rare spindle Jan 21, 2025, 11:04 PM

#

Okay

static quarry Jan 21, 2025, 11:04 PM

#

And we do this using the equation rules I just told you about.

#

(For the record, we can prove them, but the proof would probably go way over your head at this stage in your education.)

rare spindle Jan 21, 2025, 11:05 PM

#

static quarry (For the record, we can *prove* them, but the proof would probably go way over y...

Isn‘t it like straight forward

#

If someome has 10 apples

#

And the other one aswell

static quarry Jan 21, 2025, 11:05 PM

#

That's not a proof.

rare spindle Jan 21, 2025, 11:06 PM

#

But it‘s logical

static quarry Jan 21, 2025, 11:06 PM

#

Not really. I mean, it's good if you have a way to think about it that helps you come to terms with it, but that doesn't make it a proof.

rare spindle Jan 21, 2025, 11:07 PM

#

How do u actually proof it

#

I may understand it

#

Or atleast I wanna give it a try

static quarry Jan 21, 2025, 11:07 PM

#

You're not gonna understand it.

vocal eagle Jan 21, 2025, 11:08 PM

#

rare spindle How do u actually proof it

The informal "proof" is what you have and that's enough

static quarry Jan 21, 2025, 11:08 PM

#

Like, we literally have to go through Zermelo-Fraenkle set theory to Peano arithmetic to Dedekind cuts and it's a slog.

#

Like, it's very fascinating, but at your age I'm not sure you even have the brain architecture yet to understand or appreciate it.

#

And it certainly won't help you learn the material in front of you.

rare spindle Jan 21, 2025, 11:09 PM

#

static quarry Like, we literally have to go through Zermelo-Fraenkle set theory to Peano arith...

I can do abit of set theory

#

But Not much

#

Like A={1;2}

static quarry Jan 21, 2025, 11:09 PM

#

That's not set theory, that's just naming a set.

rare spindle Jan 21, 2025, 11:10 PM

#

What about the intersection of two sets

static quarry Jan 21, 2025, 11:10 PM

#

We're getting far afield.

rare spindle Jan 21, 2025, 11:10 PM

#

Draw to circles

static quarry Jan 21, 2025, 11:11 PM

#

Let's refocus back on the equations.

rare spindle Jan 21, 2025, 11:11 PM

#

Okay

static quarry Jan 21, 2025, 11:11 PM

#

static quarry Consider the equation `2x - 10 = 20 - x`.

So, looking at this equation.

rare spindle Jan 21, 2025, 11:11 PM

#

-2x?

static quarry Jan 21, 2025, 11:11 PM

#

...what do you mean by that?

rare spindle Jan 21, 2025, 11:11 PM

#

On both sides

#

Substract 2x

static quarry Jan 21, 2025, 11:12 PM

#

Hmm. Well: 2x - 10 - 2x = 20 - x - 2x

#

That is certainly still a true equation.

rare spindle Jan 21, 2025, 11:13 PM

#

Can you atleast send a picture of your magic math theory

#

I‘m rlly into math

#

I wanna understand set theory

#

Plsss

#

Only once

static quarry Jan 21, 2025, 11:14 PM

#

No. It's not in a picture, and it's not magic.

#

And it's way way way too long.

rare spindle Jan 21, 2025, 11:15 PM

#

How long?

#

2 pages?

static quarry Jan 21, 2025, 11:15 PM

#

...no, like a week.

rare spindle Jan 21, 2025, 11:15 PM

#

What is the hardest topic in math?

static quarry Jan 21, 2025, 11:15 PM

#

Getting you to stay on topic.

rare spindle Jan 21, 2025, 11:16 PM

#

Oh

#

Okay Imma focus now

#

Sorry

#

Pls go ahead

static quarry Jan 21, 2025, 11:16 PM

#

It's fine. Your enthusiasm is appreciated, it's just not very constructive if it's not directed at the problem in front of you.

static quarry Jan 21, 2025, 11:16 PM

#

static quarry Hmm. Well:``` 2x - 10 - 2x = 20 - x - 2x```

This is where we're at.

rare spindle Jan 21, 2025, 11:17 PM

#

2x-2x

#

Is

#

0.1

#

Jk

#

0

#

Or isn‘t it 0

#

?

static quarry Jan 21, 2025, 11:17 PM

#

Yes.

rare spindle Jan 21, 2025, 11:18 PM

#

Okok

#

So we get -20=x?

static quarry Jan 21, 2025, 11:18 PM

#

...no.

#

How would we get that?

#

Take it step by step.

rare spindle Jan 21, 2025, 11:18 PM

#

Oh brain lag

#

Uhm

#

-10=20-x-2x

#

And then

#

-20x

#

No no

#

-20

#

To seperate the numbers and the alphabet

static quarry Jan 21, 2025, 11:20 PM

#

Okay, stop.

#

We have -10 = 20 - x - 2x, right?

rare spindle Jan 21, 2025, 11:20 PM

#

Yes

static quarry Jan 21, 2025, 11:20 PM

#

Can we simplify this before doing anything else?

rare spindle Jan 21, 2025, 11:21 PM

#

We can bring the 20 on the other side

#

Uh wait no

#

I see

#

-x-2x is -3x

#

So we get -10=-20-3x

static quarry Jan 21, 2025, 11:22 PM

#

Right.

rare spindle Jan 21, 2025, 11:22 PM

#

And now +20?

static quarry Jan 21, 2025, 11:22 PM

#

Why?

#

Okay, stop.

rare spindle Jan 21, 2025, 11:22 PM

#

To bring the -20 on the other side

static quarry Jan 21, 2025, 11:22 PM

#

I need you to be writing this all on paper.

rare spindle Jan 21, 2025, 11:23 PM

#

I‘m sure I can do it in my head

static quarry Jan 21, 2025, 11:23 PM

#

You're already making mistakes.

#

This is what paper is for.

rare spindle Jan 21, 2025, 11:23 PM

#

Can I write on my iPad?

static quarry Jan 21, 2025, 11:23 PM

#

What were you writing those notes I gave you before on?

rare spindle Jan 21, 2025, 11:24 PM

#

On my pc

#

But my dad took it a way a few min ago

#

So I switched on my iPad

static quarry Jan 21, 2025, 11:24 PM

#

Look, write it wherever the hell you want to, just write it.

rare spindle Jan 21, 2025, 11:24 PM

#

Okok

static quarry Jan 21, 2025, 11:25 PM

#

Showing your work, visibly, all in one place, one step after another, is important.

#

Our initial equation is 2x - 10 = 20 - x.

rare spindle Jan 21, 2025, 11:26 PM

#

static quarry Jan 21, 2025, 11:26 PM

#

Okay.

rare spindle Jan 21, 2025, 11:26 PM

#

-20?

static quarry Jan 21, 2025, 11:26 PM

#

Try it.

rare spindle Jan 21, 2025, 11:28 PM

#

Like that?

#

In theory

#

If you plug in 10 for x

#

Both sides have to be equal

#

Right?

#

Oh it works

#

Yay

static quarry Jan 21, 2025, 11:31 PM

#

rare spindle Like that?

You made a mistake when dividing by 3.

rare spindle Jan 21, 2025, 11:31 PM

#

Huh

#

But the solution is correct

#

Hmm

static quarry Jan 21, 2025, 11:32 PM

#

Because you made two mistakes that cancelled out.

#

See, you should've divided by -3, and that's basically what you did, but what you wrote is division by 3, and that you did incorrectly.

rare spindle Jan 21, 2025, 11:33 PM

#

Ohhh I see

#

3/-3 is -1

#

And 30/-3 is -10

static quarry Jan 21, 2025, 11:34 PM

#

Right.

rare spindle Jan 21, 2025, 11:34 PM

#

So you get -10=-1*x

static quarry Jan 21, 2025, 11:34 PM

#

Yes.

rare spindle Jan 21, 2025, 11:34 PM

#

And only Number that satifies the equation is 10

static quarry Jan 21, 2025, 11:34 PM

#

Right.

rare spindle Jan 21, 2025, 11:35 PM

#

I understand it now

static quarry Jan 21, 2025, 11:35 PM

#

Glad to help.

rare spindle Jan 21, 2025, 11:36 PM

#

Can you teach me more math

#

Something else

#

Plss

#

I would really appreciate it learning from genuises

#

Or higher ranks

timid lark Jan 21, 2025, 11:38 PM

#

rare spindle Can you teach me more math

do you have a specific question?

rare spindle Jan 21, 2025, 11:38 PM

#

Not really

#

Js wanna learn math

#

Like further math

timid lark Jan 21, 2025, 11:41 PM

#

rare spindle Like further math

be specific.

static quarry Jan 21, 2025, 11:41 PM

#

rare spindle Like further math

You should probably wait until you have a solid grasp of, y'know, seventh grade algebra.

rare spindle Jan 21, 2025, 11:42 PM

#

timid lark be specific.

I have stumbled accross a question

#

And I wanna solve it

#

But yet I don‘t have the tools

static quarry Jan 21, 2025, 11:42 PM

#

This is gonna be the Riemann hypothesis or something, isn't it?

rare spindle Jan 21, 2025, 11:42 PM

#

I‘ve seen it on the other math server

#

#

This one

timid lark Jan 21, 2025, 11:43 PM

#

rare spindle

yeah, no, don't try this

rare spindle Jan 21, 2025, 11:43 PM

#

But one day i wanna learn it

timid lark Jan 21, 2025, 11:43 PM

#

this is way beyond a 7th grade level, much less high school

rare spindle Jan 21, 2025, 11:43 PM

#

Maybe 4 months

timid lark Jan 21, 2025, 11:44 PM

#

rare spindle But one day i wanna learn it

you learn by mastering other subjects first.

rare spindle Jan 21, 2025, 11:44 PM

#

timid lark you learn by mastering other subjects first.

But would u say it is possible in 4 months

timid lark Jan 21, 2025, 11:44 PM

#

rare spindle Maybe 4 months

if you're going to set that goal, be specific about what you want to learn in certain intervals.

#

what topics do you want completed within 1 month?

#

2 months?

#

3 and a half?

rare spindle Jan 21, 2025, 11:45 PM

#

Maybe calculus

#

I‘ve done some research

#

But

#

I don‘t know how much it is

timid lark Jan 21, 2025, 11:46 PM

#

it is a lot.

rare spindle Jan 21, 2025, 11:46 PM

#

Would u say it is possible to learn calculus within 4 months

#

Like only applying

#

Not actaully to a 1 week long proof

static quarry Jan 21, 2025, 11:47 PM

#

rare spindle Would u say it is possible to learn calculus within 4 months

Not from where you are.

rare spindle Jan 21, 2025, 11:47 PM

#

Wdym

static quarry Jan 21, 2025, 11:48 PM

#

rare spindle Wdym

I mean no, it's not possible for a seventh grader to learn calculus within 4 months.

timid lark Jan 21, 2025, 11:48 PM

#

rare spindle Would u say it is possible to learn calculus within 4 months

probably not, it took me ~5 months to learn up to calc II, and im in 10th grade right now.

#

i still have to cover calc III, in addition to linear algebra.

rare spindle Jan 21, 2025, 11:49 PM

#

timid lark i still have to cover calc III, in addition to linear algebra.

Can u solve the question I sent u?

#

timid lark Jan 21, 2025, 11:50 PM

#

rare spindle Can u solve the question I sent u?

not with my current knowledge.

rare spindle Jan 21, 2025, 11:50 PM

#

static quarry I mean no, it's not possible for a seventh grader to learn calculus within 4 mon...

Maybe 1 year?

static quarry Jan 21, 2025, 11:50 PM

#

rare spindle Maybe 1 year?

No, dude, no. Just focus on learning what you're being taught.

rare spindle Jan 21, 2025, 11:51 PM

#

timid lark not with my current knowledge.

Did you also learn proving

timid lark Jan 21, 2025, 11:51 PM

#

rare spindle Did you also learn proving

"proofs", not too much, but as techie said, focus on the basics.

rare spindle Jan 21, 2025, 11:52 PM

#

May I ask how old are you

#

Techie

prime prairieBOT Jan 22, 2025, 5:22 AM

#

wrong channel bozo. Go to #geonosidan-prison-complex

#How do I solve equations?