Question

Bit confused.... Why do I divide by 3?

3|x + 6| = 36

Answer 1

You would multiply 3 to x and 6
3x+18=36
minus 18
3x=18
divide by 3
x=6

Answer 2

disagree
First divide by 3

Answer 3

wait i dont think thats how you do it

Answer 4

why do you divide?

Answer 5

ok soooo we are trying as much as possible to alienate the absolute value

Answer 6

and then once we have just the absolute value isolated on one side of the equation we can the solve for absolute value regularly such as
(x+6)=13
and
(x+6)=-13

Answer 7

Dividing simplifies the equation and it's calculations.
P.S. it's 12 not 13.

Answer 8

You apply the opposite operations when you move the numbers/variables to the other side.
So,
3x+6=36
3x= 36-6
3x=30
x=30/2
x=15.

Get it?

Answer 9

why isn't it 36 minus 3? instead of division?

Answer 10

Sorry you are correct:
(x+6)=12
and
(x+6)=-12

Answer 11

lots of different answers.....

Answer 12

so whatever number is to the left of an absolute value you ALWAYS divide to the other side of the equal sign?

Answer 13

\[\left| x+6 \right|=\pm \left( x+6 \right)\]
solve taking both cases.

Answer 14

but why do you divideeeeeeeeeeeeeee

Answer 15

you divide because 3/3 = 1

Answer 16

but i thought you can only add or subtract the number from the left of the equal sign to the right of the equal sign

Answer 17

\[3a = b\]
\[\frac{3}{3}a = \frac{b}{3}\]
\[1a = \frac{b}{3}\]
\[a = \frac{b}{3}\]

Answer 18

no, you can work any mathimatical operation you want to.

Answer 19

the idea is to use the same operation on both sides in order to keep things equal.

Answer 20

can you multiply too?

Answer 21

is multiplication a mathimatical operation?

Answer 22

yea

Answer 23

then yes ....

Answer 24

dividing by 3 is the same as multiplying by 1/3

Answer 25

*sigh* im so confused right now i thought in algebra you cant divide the other side unless it was like a 3x

Answer 26

it is 'like' 3x

Answer 27

3|x+6|

realise that |x+6| is just some number ... let it be equal to a

3a

Answer 28

hmmmm so okay this problem wont work without division?

Answer 29

itll work with any mathimatical operation you want to perform.

but dividing off the 3 is the fastest way to approach it

Answer 30

we could multiply by 2 if we wanted to, but it doesnt really do much to help us solve the problem in a timely fashion

Answer 31

we could add 5/16 but that doesnt really do us much in the way of getting to a solution quickly

Answer 32

its 3 because its the lowest common denominator right?

Answer 33

its 3 because you have: 3, times, something

if we had 1, times, something ... things would move quicker for us

since 3/3 = 1, we should divide it all by 3

Answer 34

what if it was 25|x + 6| = 30

Answer 35

would it be 5|x + 6| = 6

Answer 36

thats fine too, or

25, times, something

this would be easier if we had: 1, times, something

since 25/25 = 1, we should do what?

Answer 37

30/25 = 6/5 so either approach you take

Answer 38

doesnt it have to be 5 on each side?

Answer 39

since thats the lowest multiple?

Answer 40

no, it doesnt 'have to be'

Answer 41

nowhere in this conversation has anyone mentioned that you have to use some lowest multiple.

Answer 42

all youve done is modify the form to: 5|x+6| = 6

you still have to divide off another 5

Answer 43

so you have to carry the 25 and divide it to 30?

Answer 44

and you divide 25 by 25?

Answer 45

so it would be |x +6| = 30/25?

Answer 46

you want to create the situation where you have: 1|x+6| on the left side

Answer 47

so dividing 25 by 25 gets us to that situation.

Answer 48

ohhhhhhhhhhh okay i get it

Answer 49

thanks!

Answer 50

good :) youre welcome