Question

6a(4+6z)= 1+9

Answer 1

Eyyy, sup?
We solving for z or something?

Answer 2

Need some directions :3

Answer 3

its b

Answer 4

yes please :) @zepdrix

Answer 5

\[\Large\rm 6a(4+6z)=1+9\]Add the 1 and 9, ya?\[\Large\rm 6a(4+6z)=10\]We COULD distribute the 6a to each term in the brackets, but that creates more work for us.
Notice that the 6a is `multiplying` the brackets.

Answer 6

Let's do the inverse, let's divide 6a to the other side k?

Answer 7

ok

Answer 8

so you would et 1.67a right??

Answer 9

on the right side

Answer 10

haha what do you mean :P @Nnesha

Answer 11

\[\Large\rm \frac{\cancel{6a}(4+6z)}{\cancel{6a}}=\frac{10}{6a}\]\[\Large\rm (4+6z)=\frac{10}{6a}\]No no careful! :)
Notice that the a is stuck in the bottom.
We can't call it 1.67a.
Maybe we just leave it like this, so there is no confusion.
Now we have nothing being applied to the brackets, we can just ignore them.\[\Large\rm 4+6z=\frac{10}{6a}\]

Answer 12

And continue to isolate the z :O
It has a 4 being added ya? How we undo that?

Answer 13

we subtract 4?

Answer 14

\[\Large\rm 6z=\frac{10}{6a}-4\]Mmm k good,
just gotta undo that last multiplication step now :)

Answer 15

ok so your talking about the 6z right??

Answer 16

Yes, the 6 is multiplying z,
we want to undo that in order to get our z alone.

Answer 17

ok so we divide 6to both sides?

Answer 18

Yes. Since we already have a fraction on the right side, it's going to look a little weird.
Do you understand how to divide that first fraction by 6?

Answer 19

not really haha

Answer 20

Umm ok, maybe here is an easier way to think of it.
When you see a fraction like this:\(\Large\rm \frac{1}{5}\)
try to get in the habit of thinking of that as a division operation.
Yes, we're multiplying by 1/5, but what we're really doing is dividing by 5, because there is a 5 in the bottom.

So another sneaky way we can divide both sides by 6 is to multiply both sides by 1/6.

Answer 21

\[\Large\rm \frac{1}{\cancel6}\cdot \cancel6z=\left(\frac{10}{6a}-4\right)\frac{1}{6}\]

Answer 22

oh ok i see what youu did :)

Answer 23

so thats the final answer right??

Answer 24

We'll give that 1/6 to each term in the brackets,\[\Large\rm z=\frac{10}{6a}\cdot\frac{1}{6}-4\cdot\frac{1}{6}\]You remember how to multiply fractions? :o

Answer 25

i think so... you would multiply -4 to the top and bottom?? or no haha :P

Answer 26

-4 is the same as -4/1.
With fraction multiplication we do `top with top`, `bottom with bottom`, ya? :)
So it looks like ONLY the top will get a -4.

Answer 27

oh ok :) i was close... :P

Answer 28

\[\Large\rm z=\frac{10}{6a}\cdot\frac{1}{6}-\frac{4}{6}\]And we do same with the first term, multiply top with top, bottom with bottom, giving us,\[\Large\rm z=\frac{10\cdot1}{6\cdot6a}-\frac{4}{6}\]
\[\Large\rm z=\frac{10}{36a}-\frac{4}{6}\]

Answer 29

And then I guess the only last little step you might want to do is to simplify the fractions :o
We have a bunch of even numbers, so they should simplify a bit.

Answer 30

So it would be z = 5/18 -2/3 right??

Answer 31

yay good job \c:/

Answer 32

Woops, `a` still in the bottom of the first fraction*

Answer 33

so do we have to do something about that??

Answer 34

Nah, that's just how the problem worked out :)\[\Large\rm z=\frac{5}{18a}-\frac{2}{3}\]