Question

Algebra Question

Answer 1

If \[\frac{ a }{ 2 } + \frac{ b }{ 2 } = 3 \] what is the value of 2a +2b?

Answer 2

I haven't really been able to get anywhere on it, any form of help will help :D

Answer 3

u still there

Answer 4

what do u think

Answer 5

yeah im back sorry

Answer 6

@slade well I don't really have any idea on how to start

Answer 7

I dare you to multiply both sides by 4

Answer 8

thats how u do it right there

Answer 9

double dog dare you

Answer 10

what would that do? um okaay 3 x 4 = 12 on the right but i don't know how to multiply the fractions :/

Answer 11

do you know what 4/2=?

Answer 12

yes 2

Answer 13

\[4(\frac{a}{2}+\frac{b}{2}) \\ =\frac{4}{2}a+\frac{4}{2}b=? \]

Answer 14

a/2 and b/2 x 4?

Answer 15

yes

Answer 16

ah gotcha

Answer 17

2a + 2b is what i get! and that means it eqauls 3 !!

Answer 18

no

Answer 19

3(4)

Answer 20

but what would make me multiply each side by 4?

Answer 21

oh yeah 12

Answer 22

to solve for 2a+2b

Answer 23

I like your approach @freckles

Answer 24

2 * 4 =?

Answer 25

I dare you all to learn math :-D double dog dare at that :-D

Answer 26

to solve yes but where did you think of 4 why not 3? like is there a specific reason or thats just how algebra works? common factor what was it?

Answer 27

well 4(a/2+b/2)
would give me what I want which is 2a+2b

Answer 28

i'm trying nixy lol

Answer 29

but if I multiply one side by 4 I have to multiply the other side by 4

Answer 30

ah yes that is true that is how to get the end result

Answer 31

do you want to give you a problem that is similar ?

Answer 32

sure

Answer 33

@kevinhunterwood69 it is hard work but if you keep at it, it will get easier :-D

Answer 34

yeah i am

Answer 35

solve for 6a+9b
given
\[2a+3b=-1\]

Answer 36

im out

Answer 37

no one is listening to me

Answer 38

lol there

Answer 39

goodbye @slade :(

Answer 40

@kevinhunterwood69 do you notice how to find the value of 6a+9b yet?

Answer 41

okay so I did:
solve for 6a + 9b
given: 2a + 3b = -1
work:
2a + 3b = -1
3 (2a + 3b) = -1(3)
6a + 9b = -3
answer: -3

Answer 42

was that correct?

Answer 43

omg brilliant

Answer 44

yay :D

Answer 45

math is fun when i can finally understand algebra

Answer 46

good job
I bet if that was the problem you had you would have had no problems
do you think the fractions throw you off ?

Answer 47

yes def fractions have always been a struggle to understand

Answer 48

square roots too but mostly fractions

Answer 49

try this one:
\[\text{ If } a+\frac{b}{3}=4 \text{ then what is the value of } 21a+7b\]

(this will has a fraction in it; let's see if it throws you off any this time )

Answer 50

hmm

Answer 51

if i move 3 to the other side will it be on top?

Answer 52

actually wait i can't do that right ugh um if i move b let me see

Answer 53

so you want to multiply both sides 3 to remove the fraction
you can do that
3a+b=12
but we still are not done

Answer 54

all i know is im trying to get constants on one side and variables on the other right?

Answer 55

sorry what

Answer 56

how did you get 3a and b lost its 3? oh you moved the 3 from b next to a?

Answer 57

\[a+\frac{b}{3}=4 \\ \text{ if you don't like the fraction there you can always multiply both sides by } \\ \text{ what is \in the denominator of that fraction } \\ 3(a+\frac{b}{3})=3(4) \\ 3(a)+3(\frac{b}{3})=3(4) \\ 3a+b=12\]

Answer 58

yes that explains it! thanks so much

Answer 59

well 3a i understand actually haha 3(b/3) = b?

Answer 60

\[3(\frac{b}{3})=3 \cdot \frac{b}{3}=\frac{3}{1} \cdot \frac{b}{3}= \frac{3}{3} \cdot \frac{b}{1}=1 \cdot b =b \]

Answer 61

basically in summary 3/3=1 so you are left with 1*b which is just b

Answer 62

like in your problem we had above we had:
\[\frac{a}{2}+\frac{b}{2}=3 \\ \text{ we could have cleared the fractions before finding what we wanted } \\ \text{ by multiplying both sides by 2} \\ 2(\frac{a}{2}+\frac{b}{2})=2(3) \\ 2 \frac{a}{2}+2 \frac{b}{2}=2(3) \\ a+b=6\]

Answer 63

yes i follow up to the point 3/3 = b/1 why does b not become 3b? like 3/3 = 3b/1 ?

Answer 64

anything over itself is 1

(well except 0)

Answer 65

well 3/3 *b =b

Answer 66

first do you know that 3/3=1 ?

Answer 67

yes i do

Answer 68

no time for jokes lol

Answer 69

\[\frac{3}{3}=1 \\ \text{ so if I multiply both sides by } b \text{ we have } \\ \frac{3}{3}b=1 b\]

Answer 70

yes

Answer 71

is this not answering your question?

Answer 72

no it did

Answer 73

so we were at 3a + b = 12

Answer 74

and m trying to figure out what is 21a + 7b so

Answer 75

right and we want 21a+7b 's value

Answer 76

yes

Answer 77

any if you multiply both sides by s_v__ you will get?

Answer 78

I didn't put the full word there

Answer 79

ah seven

Answer 80

wait a second

Answer 81

then we multiply 12 by 7 that means :O

Answer 82

yep! :)

Answer 83

just so you know we could have figured out 21a+7b in one step

Answer 84

instead of two

Answer 85

ya so 21a + 7b = 84

Answer 86

\[a+\frac{b}{3}=4 \\ \text{ we wanted } 21a+7b \\ \text{ so we could have just multiplied 21 on both sides \to \begin with } \\ 21a+21(\frac{b}{3})=21(4) \\ 21a+7b=84\]

Answer 87

wow

Answer 88

anyways keep practicing
and numbers will become easier to play with

Answer 89

thanks for all the extra practice!

Answer 90

np :)
these can get a lot funnier I promise

\[\text{ assume } a \text{ and } b \text{ are positive } \\\text{ if } a^2+2ab+b^2=4 \text{ then what is } (a+b)^4 \text{ or what is } a+b \]
I think they can even get funnier than that

Answer 91

uh lol

Answer 92

\[a^2+2ab+b^2=(a+b)^2 \text{ is the trick there }\]

Answer 93

ah

Answer 94

welp i'll go back to this sat book

Answer 95

k k
have fun :)

Answer 96

and ponder on about the funny stuff in math lol

Answer 97

thx frecks