Question

solve m=2x+3y for y?

Answer 1

y=m-2x/3

Answer 2

Alright, I'll need your input to solve this, italian. You ready for this?

Answer 3

y=(m-2x)/3

Answer 4

Just giving them the answer won't help them learn lol
You've gotta let them work through the answer. :P

Answer 5

lol uber. sorry. shall delete my answer.

Answer 6

Just giving them the answer won't help them learn lol
You've gotta let them work through the answer. :P
absolutely agree with this.

Answer 7

Italian? Still here? We need to work through this if you wanna learn the steps. :P

Answer 8

yeah im here

Answer 9

Awesome!
So which letter do we want by itself?

Answer 10

y

Answer 11

perfect!

m=2x+3y

Answer 12

First thing we want is for y to be positive. Is it?

Answer 13

awesome! So this means we won't be subtracting y and that we'll be leaving it on the right side of the equals sign so that it stays positive. Now, we want y by itself. What is currently bothering it?

Answer 14

Here's the equation again:
m=2x+3y

Answer 15

Yup! Now, here's the thing: for now we'll make believe that the 3 and y are buddies and don't want to separate.

Answer 16

However... someone else is being really annoying. Who is that?

Answer 17

Indeed. How do we make the 2x go away?

Answer 18

Well, if we do that, we'd have to divide *everything* by 2x. That'd give us:
m/2x = 3y/2x

Answer 19

do we really want this?

Answer 20

Note that 2y just got even closer to that 2x that was annoying him. :(

Answer 21

no should you subtract?

Answer 22

Perfect! So how will our equation look?

Answer 23

m-2x=3y?

Answer 24

Perfect!

Answer 25

Now y can finally be by himself after one more step.

Answer 26

then you divide both sides by 3 right?

Answer 27

Heck ya! :D

Answer 28

And what's our final answer? This step can be tricky.

Answer 29

haha thanks a lot

Answer 30

No problemo. Go ahead and add the finishing steps just to make sure we've got this. ^_^

Answer 31

very close. Remember you have to divide everything by 3.

Answer 32

There was one variable that you forgot to divide by 3.

Answer 33

perfect!

Answer 34

Alternatively, if you felt like it, m/3 - 2x/3 = y can also work :D

Answer 35

Feel free to post another problem like this as a question to be on the safe side! More practice = more 100s! :P

Answer 36

Of course. Feel free to make up a new separate question. :D

Answer 37

You mean a different letter? It's already solved for t :P

Answer 38

Ah ok.

Answer 39

Well, let's start by trying to make r be less cramped. It's dangerous to work with things inside of parenthesis, so we should try to keep that for later.

Answer 40

So... what CAN we do for now?

Answer 41

Here's a hint with something similar:

5 = (3+7)/2

Answer 42

Well, here's the thing:
The example I showed is using totally different numbers, but is in the same general 'form' as your question, right?

Answer 43

numbers in parentheses divided by a single number = another number, yes?

Answer 44

In my example, the 7 is the equivalent to the P that we want to separate in your example. Does that part make sense?

Answer 45

If it doesn't make sense, do let me know, and I'll explain it.

Answer 46

here is the equation a different way \[t=p/6+3r/6\]

Answer 47

To be honest, the original form of (p+3r) is to your advantage. However, it can also work here if you know the trick.

Answer 48

Okie dokie.

Answer 49

So going back to my 'similar example', we want to separate the 7, right?
5 = (3+7)/2

What can we do to my example to make the right side less messy?

Answer 50

multiply by 2?

Answer 51

perfect :D

Answer 52

and what does that give us so far in my example?

Answer 53

hold on

Answer 54

10=(3+7)

Answer 55

Yup!
Now that (3+7) is by itself, what can we get rid of?

Answer 56

get rid of the ()

Answer 57

Yup!
and then how do you get the 7 by itself when you have 10 = 3+7?

Answer 58

subtract the 3 from both sides

Answer 59

Awesome. I lost your original problem. lol
Could you repost it?

Answer 60

The one with the P?

Answer 61

t=(p+3r)/6 for r

Answer 62

awesome. So what's the easiest way to make it look less ugly?

Answer 63

multiply both sides by 6

Answer 64

Indeed. What do we get?

Answer 65

6t=p+3r

Answer 66

yup! Now who is annoying our buddy r? (I think we were solving for r, right?)

Answer 67

Hint: always remove items that can be moved easily to the other side first.

Answer 68

yes and the friend p

Answer 69

Yup. Make that p buzz off. We hate that guy.

Answer 70

6t-p=3r?
then divide both sides by 3 to get the answer?

Answer 71

Yessssshhhhhh

Answer 72

BUT, here's a tip: always check your answers.

Answer 73

t=(p+3r)/6 for r

Answer 74

let's plug in numbers to make this work. Let's make the parentheses equal 12 so that t can equal 2. That way we'll have 12/6 =2

Answer 75

what we can do is... make r equal 2 and p equal 6. Make sense?

Answer 76

yes

Answer 77

awesome. Could you go ahead and test it out for me, then? (Your answer, that is)

Answer 78

here's what you came up with:
6t-p=3r
turns into
r = 2t - p/3

Answer 79

so is 2 = 2(2)-6/3 ?
Or 2 = 4-2?

Answer 80

All is well? ^_^