Question

What is the solution to the following equation?
1/3 (p+9)=3+2(p-6)

Answer 1

@iGreen

Answer 2

\[\large{\cfrac{1}{3} (p+9) = 3 + 2(p-6)}\]

Answer 3

First thing first... I don't like that 1/3 stuff, so lets multiply by 3 on both sides of `=` sign.

Answer 4

What do we get?

We get :

\[\large{p+9 = 3(3+2(p-6))}\]

Answer 5

Any doubt ?

Answer 6

No

Answer 7

Good...

Now, lets simplify that a little bit more...

\[\large{p + 9 = 3 * 3 + 3 * 2 * (p-6)}\]

\[\large{\implies p + 9 = 9 + 6 * (p-6)}\]

Answer 8

Clear ?

Answer 9

@vishweshshrimali5 That's one way to do it..

We could just distribute 1/3 into the parenthesis:

\(\dfrac{1}{3} (p + 9) \rightarrow \dfrac{1}{3}p + 3\)

Plug that back in:

\(\dfrac{1}{3}p + 3 = 3 + 2(p - 6)\)

Now distribute 2 into the parenthesis, do you know how to do that? @-EtherealEbullience

Answer 10

Yep... its just that... writing fraction in latex takes more time ;)

Answer 11

Lol

Answer 12

1/3p+3=3+2(12p)?

Answer 13

Did you forget something ??

Answer 14

\[\large{a * (\color{red}{x} + \color{green}{y}) = a\color{red}{x} + a\color{green}{y}}\]

Answer 15

No..distributing 2 will give us:

\(2(p - 6) \rightarrow (2 \times p) + (2 \times -6)\)

Answer 16

Oh

Answer 17

Yep... so what would you get ?

Answer 18

9?

Answer 19

No..

Answer 20

How did you get that?

Answer 21

Can you multiply these?

\(2 \times p\)

\(2 \times -6\)

Answer 22

-12

Answer 23

Good...

Answer 24

Now :

\[\dfrac{1}{3}p + 3 = 3 + 2*p - 12\]

Answer 25

Can you solve this ?

Answer 26

1/3p+3=27p?

Answer 27

27 ?

How ?

Answer 28

\[\dfrac{1}{3}p + 3 = 3 + 2*p - 12\]

Lets see...

I am going to leave all the `p's` alone.

So:
\[\dfrac{1}{3}p + \color{red}3 = \color{red}3 + 2*p - \color{red}12\]

I am going to simplify only the red colored part

Answer 29

Sorry, its this:

\[\dfrac{1}{3}p + \color{red}3 = \color{red}3 + 2*p - \color{red}{12}\]

\[\implies \cfrac{1}{3}p = (\color{red}{3-12-3}) + 2*p\]

Answer 30

What is the value of the red coloured part ?

Answer 31

-12

Answer 32

Great !!

Answer 33

So, we have:

\[\implies \cfrac{1}{3}p = (\color{red}{3-12-3}) + 2*p\]

\[\implies \cfrac{1}{3}p = -12 + 2p\]

Now lets multiply by 3 both sides

Answer 34

We get:

\[\large{3*\cfrac{1}{3} * p = 3 * (-12 + 2*p)}\]

\[\large{\implies p = 3*(-12) + 3 * 2*p}\]

\[\large{\implies p = -36 + 6p}\]

\[\large{\implies p + 36 = 6p}\]

Any doubt in any step ?

Answer 35

No

Answer 36

Good.

So, we have:

\[\large{p + 36 = 6p}\]

\[\large{36 = 6p - p}\]

\[\large{5p = 36}\]

Answer 37

Now lets divide by 5 on both sides

Answer 38

5/36

Answer 39

Why ?

Answer 40

. . .Because that's an answer choice. And you can't simplify it anymore. . .

Answer 41

See:

\[\large{\color{red}{\cfrac{1}{5}} * 5p = \color{red}{\cfrac{1}{5}} * 36}\]

\[\large{\implies p = \cfrac{36}{5}}\]

Answer 42

^^

Answer 43

. . . : I

Answer 44

\(\dfrac{36}{5} = 7.2\)

Answer 45

Well, there we go :)

Answer 46

. . . x3 Thank you.

Answer 47

Your welcome :)