Question

ab=c
Solve for a
Do i need to divide both sides by b?

Answer 1

yes

Answer 2

And that is all?

Answer 3

yes, so when you do that what will you get?

Answer 4

a=a?

Answer 5

\[\frac{ab}{b}=\frac{c}{b}\]
\[a=\frac{c}{b}\]

Answer 6

Oh! now i get it, can you set up another example so i can try?

Answer 7

Sure ax+y=c, solve for x

Answer 8

Ok, divide ax with a, then divide c with a getting ax/a+y=c/a.
You then simplify that getting x+y=c/a.
Then you take both sides minus y getting x=c/a-y

Answer 9

Is this correct?

Answer 10

Really close but we need to either get rid of the y first before divide or also divide the y by a

Answer 11

YES! Thanks for teaching me :)

Answer 12

aw :(

Answer 13

No, first start by subtracting y from both sides

Answer 14

Alright, so ax+y=c
ax=c-y
x/a=c/a-y
x=c/a-y

Answer 15

remeber that when you divide the a you need to do it to all the terms

Answer 16

Where did you get z?

Answer 17

Oh right.. so x=c-y/a

Answer 18

\[x=\frac{c-y}{a}\]

Answer 19

zbay is correct

Answer 20

Inopeki got the answer i just put it in the equation maker for ease of the viewers

Answer 21

Yay! :D

Answer 22

inopeki you need to write x=(c-y)/a just to make it clearer. i see it now good work

Answer 23

Thanks for the help :) Is there any way you can make it a little harder to give me a challenge?

Answer 24

yea i will come up with one for you

Answer 25

Thanks.

Answer 26

\[\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\]

Solve for T_2

Answer 27

umm.. ill try

Answer 28

Nobody mentioned division by zero ?!!

Answer 29

Good observation @ Foolformath

Answer 30

Well to begin with i need to multiply both sides with P2V2, getting P1V1/T1*P2V2, right?\[P _{1}V _{1}divT _{1}+P _{2}V _{2}=T2\]

Answer 31

I'll lay it out by steps for you

Answer 32

NOO. wait. Its

Answer 33

Cross multiplication

Answer 34

P1V1/T1*P2V2=T2

Answer 35

lcd = T_1T_2

\[T_2P_1V_1=V_2P_2T_1\]
\[T_2=\frac{V_2P_2T_1}{P_1V_1}\]

Answer 36

Oh right, i see it now. You wanted me to put the things i was multiplying by(V2P2) in by the other things that were multiplied. That would mean my answer is right, but yours is simplified.

Answer 37

No?

Answer 38

No because you need to multiply both sides by the lcd of \[T_1T_2\] first then we cancel one of the varibles out because they are the same on top and bottom. then we can break T_2 apart from the rest of the left side by division, your answer would look close but in the end it would be wrong

Answer 39

What is an lcd? What makes T1 jump up?

Answer 40

lcd= lowest common denominator

Answer 41

What is that?

Answer 42

Is a denominator the 1 in T1?

Answer 43

The denominator is what is on the bottom of the fraction, so when we do the left side we get
\[\frac{T_1T_2P_11V_1}{T_1}\]
and because we have the same thing on the top and bottom we can cancel out the denominator leving us with
\[T_2P_1V_1\]
and we do the same operation on the right side

Answer 44

Why do we get T1 on both sides of the line?

Answer 45

because you are multiplying by t1t2 but on each side one of them will cancell

Answer 46

Ah

Answer 47

Good job that was a hard one

Answer 48

Thanks, when am i going to get to learn this in school?

Answer 49

what grade are you?

Answer 50

8th

Answer 51

Not sure when you will cover that but it's a chemistry equation compariing similar gasses to determine preasure, temp, or volume. You might touch it in highschool sometime.

Answer 52

Oh, cool. What should i do now?

Answer 53

PV=nrt solve for n

Answer 54

And then try this \[V=\frac{4}{3}\pi r^3\] Solve for r

Answer 55

Divide both sides by rt, getting PV/rt=n, am i right? By the way, why is PV upper case?

Answer 56

Zed, isnt that for volúmes of spheres or something? exept r should be ^3

Answer 57

good question and i don't have an answer for you but in that equation they are all upercase but the little n but i made a mistake and didn't capitilize the RT

Answer 58

But was i right?

Answer 59

Zed, im going to do yours now.

Answer 60

yes you were right and that was the ideal gas law by the way

Answer 61

Oh, that was a ^3! Divide both sides with (pi)r^2 getting V/(pi)r=4/3r, am i right sofar?

Answer 62

What does the law state?

Answer 63

okay so first step is to get r^3 by itself. what do you get?

Answer 64

http://en.wikipedia.org/wiki/Ideal_gas_law

Answer 65

Wait. I take back my first answer. First you divide both sides by 4/3(pi) to isolate r^3

Answer 66

good. have you done powers before and their inverses?

Answer 67

I think so, what do you mean?

Answer 68

okay so we have \[r^3=\frac{3V}{4}\]
how do I get rid of the cubed part?

Answer 69

Oh, i have done powers but i dont recall doing inverses, is that like squareroot and cubicroot? I guess we need to get the "cubicalroot" out of r^3.

Answer 70

We should be able to just divide r by r 2 times.

Answer 71

3* and by itself i mean the root.

Answer 72

not quite see let's try this example to help explain it

\[x^2=4\]\[x=\sqrt{4}\]\[x=4^{\frac{1}{2}}\]\[x=2\]

Answer 73

What? Can you explain that?

Answer 74

okay so when we bring powers (eg 3) over the equation sign they turn to 1/powers (eg 1/3).

if we look at squared when we bring it over it turns to 1/2 which is also known as the square root.

Answer 75

Why does it become 1/2?

Answer 76

the may be abit hard to follow but this is why.
Let f(x)=y

\[y=x^7\]
\[\ln y=7 \ln x\]
\[lnx=(lny)/7\]

\[x=e^{(lny)/7}\]
\[Inverse = f^{-1}(x)=e^{(lnx)/7}\]

\[ f^{-1}(x)=e^{lnx^\frac{1}{7}}\]\[=x^\frac{1}{7}\]

Answer 77

Now usually when learning this we just accept this as fact that \[x^n=x^{\frac{1}{n}}\] where n is a positive integer

Answer 78

That was probably way too much information at once just use the rule in the above post and try to solve \[r^3=\frac{3V}{4}\]

Answer 79

So if r^2 becomes 1/2, then r^3 should become 1/3, right?

Answer 80

Correct

Answer 81

That means that i have to maake r^3 to 1/3 and convert 1/3 to 4/12(to merge it with the right side). i then convert the right sides fractions too, getting 9V/12. Now i should be able to merge them, right? so i get r=13/12?

Answer 82

I screwed that up right...

Answer 83

What?

Answer 84

Sorry we want to raise both sides by the power of (1/3)

Answer 85

r^1/3=3V^1/3/4?

Answer 86

so the left hand side will be \[(r^3)^{\frac{1}{3}}=r^{\frac{3}{3}}=r^1=r\]

Answer 87

I dont understand.

Answer 88

okay the right side is good. we have \[(\frac{3V}{4})^\frac{1}{3}\]

Answer 89

remember on the left hand side we had r^3 and when raised it to the power of 1/3 the powers need to be multiplied.

Answer 90

Oh! So its r^3*1/3?

Answer 91

yes exactly it's one of the rules for powers.

here are others if you wanted to learn and practice http://www.math.com/school/subject2/lessons/S2U2L2DP.html

Answer 92

So the answer is r^3*1/3=3V^3/4

Answer 93

yes and that simplifies to r=(3V/4)^1/3

Answer 94

Oh!

Answer 95

Well I'm off to sleep. I'll be on tomorrow if you want more examples or help :)

Answer 96

Thanks for everything!