Question

Please help me with solving an equation! I'll fan and medal



8-2b=-2/3(12 b+6)

Answer 1

@whpalmer4

Answer 2

I need an explanation

Answer 3

and it's not 3, it's -2

Answer 4

(I just don't know how to get that answer)

Answer 5

\[8 - 2b = -\frac{ 2 }{ 3 } (12b+6)\]
The first thing you want to do is to get rid of the fraction :)
So multiply both sides by 3. Like this:
\[3 ( 8 - 2b) = 3 \times -\frac{ 2 }{ 3 } (12b+6)\]

Answer 6

now what would you get when...
\[3 \times -\frac{ 2 }{ 3 } = ?\]

Answer 7

-2?

Answer 8

excellent! So now we know this:
\[3 (8-2b) = -2 (12b + 6)\]
Now we want to get rid of the brackets so expand the brackets

Answer 9

(12b + -2) x (6+-2)? i'm not sure

Answer 10

hmm...not quite.
OKay, let's just focus on everything on the LEFT side of the '=' sign.
\[3 (8 - 2b)\]
So to expand this, we multiply everything in the brackets by 3.
\[3 ( 8 - 2b) = (3 \times 8 ) - (3 \times 2b)= ?\]

Answer 11

what does 3 times 8 = ?
And what does 3 times 2b = ?

Answer 12

24 and 6b?

Answer 13

yeeess! So then,
\[3 ( 8 - 2b) = 24 - 6b\]

So that's the left side covered of the equation:
\[3( 8 - 2b) = -2 ( 12b + 6)\]

Now if we look at the right side of the = sign, we have:
\[-2 ( 12b + 6) = ?\]
Can you expand this one (think of it like -2 times 12b PLUS -2 times 6) ?

Answer 14

(-2 x 12b) + (-2 x 6)

Answer 15

yepp and what would that equal to?
-2 x 12b = ?
-2 x 6 = ?

Answer 16

-24b and -12? I have a question too, does it matter if the terms are unlike when adding and subtracting/ multiplying and dividing?

Answer 17

that's correct! So now we know,
\[-2 ( 12b + 6) = -24b - 12\]

So if we put it all together, this is what we have done:
\[8 - 2b = \frac{ -2 }{ 3 } (12b + 6)\]
We wanted to "get rid of the fraction" so we multiplied both sides by 3
\[3 ( 8 - 2b) = 3 \times - \frac{ 2 }{ 3 } (12b + 6)\]
\[3 ( 8 - 2b) = -2 (12b + 6)\]
Then we expanded the brackets or "multiplied everything out"
\[24 - 6b = -24b - 12\]

Now from here, you just want to collect like terms :)

Answer 18

Ok so 6b-24b-24-12?

Answer 19

what happened to your equal sign?
\[24 - 6b = -24b - 12\]
Add 24b to both sides:
\[24 - 6b + 24b = -24b - 12 + 24b\]
Simplify & collect like terms

Answer 20

so, 24 - 6b + 24b = ?

and then -24b - 12 + 24b = ?

Answer 21

Are we adding -24b on both sides?

Answer 22

we are adding +24b on both sides
(so this way, we can get rid of the -24b on the right side)

Answer 23

so 36b?

Answer 24

what does 24 - 6b + 24b = ?

Answer 25

e.g. 24 - 6bananas + 24bananas = ?
(you want to collect like terms so only the bananas can be grouped together).
24 - 6bananas + 24bananas
= 24 + 18bananas
right?

so the same thing applies here.
24 - 6b + 24b
= 24 + 18b

Answer 26

now, what does
-24b - 12 + 24b = ?
You can rearrange this equation if it is easier for you:
24b - 24b - 12 = ?

Answer 27

-12?

Answer 28

YES! :DSo now,
24 - 6b = -24b - 12

Then we added +24b to both sides:
24 - 6b + 24b = -24b - 12 + 24b

We collected like terms:
24 + 18b = -12

The next step is to isolate the 18b because we want to find out what "b" equals to right?
(We want something that looks like 18b =...)

SO we need to SUBTRACT 24 from both sides.
24 + 18b - 24 = -12 - 24
18b = -12 - 24

What does -12 - 24 = ?

Answer 29

-36?

Answer 30

yaaaa. So,
18b = -12 - 24
18b = - 36
We have 18b but we only need to find out what "b" equals to.
Divide both sides by 18 and you're done!