Question

I don't understand this at all, nor where to start please help?

P = 2L + 2W for L

Answer 1

hey, a good place to start is to think about what we need to do to get L by itself

to do this, we are going to need to know what opposite equations are. We know that the opposite of addition is subtraction and the opposite of multiplication is division

Answer 2

Still confused..

Answer 3

so we are going to apply that knowledge and do the following steps:

P - 2W = 2L +2W - 2W
we do this because whatever we do to one side of the equation we have to do to the other side of the equation

so +2W and -2W cancel and we are left with:

P-2W = 2L

Answer 4

then we still dont have L completely by itself, so we need to do the opposite of multiplying by 2 and we need to divide by 2 that will give us this:

(P-2W)/2 = 2L/2

Answer 5

but since we were doing an opposite equation, we can cancel the twos on the right side and we are left with:

(P-2W)/2 = L

Answer 6

they're completely different variables though, does it still not matter and we have to apply the same steps as to linear equations for example?

Answer 7

not sure if i made myself clear enough..

Answer 8

sorry, had to talk to someone for a minute. You are correct about them not mattering. Even though they are different variables, we can still treat them like numbers. We don't know anything about those numbers, but we do know that they are numbers.

Using the same steps as linear equations will give you the correct answer.

Answer 9

it's okay, i think i may get it.. would i be correct as well if my answer came to be L = (P-W)/2
or do i still need to take a few steps?

Answer 10

that is almost correct, but what happened to the 2 that was attached to the W?

Answer 11

I put P-2W= 2L + 2W-2W -> P-2W=2L <- Divided that by 2. Then I got..
L=(P-W)/2..

Answer 12

I did not make myself so clear did I?

Answer 13

close, however, when you divide by the 2 that is attached to the L, it needs to get applied to everything so you can get either:

L = P/2 - W

or

L = (p-2w)/2

the reason being that if you divide everthing by 2 it would look like this:

L = P/2 - 2W/2

from here we can either pull the /2 outside of a parenthesis, or we can apply it to each term individually

Answer 14

So in either answer the W would have to keep it's coefficient?

Answer 15

meh.. i'm so lost sorry ..

Answer 16

haha, no worries, that's what we're here for

well, yes and no. W keeps it's coefficent depending on what order you do your operations. Like I said up there^, another possible answer is :
\[L = \frac{P }{ 2 } - W\]

Answer 17

this is why these equations bother me.. hah.. the thought of the equations having more than 1 answer and not knowing which is the correct one.

In this case, which IS the correct one, or are both valid answers?

Answer 18

both of them are technically the same answer, but written in different ways

\[L=\frac{P-2W}{2}\]
this answer does not apply the division of two to each term individually, but instead applies it to the whole side and says screw it, that's goood enough.

\[L=\frac{P}{2}-W\]

this answer applies the division to both terms individally and sees what falls out of that.

Answer 19

I think I understand now. Thanks a lot. :D

Answer 20

no problem! sorry if I was hard to understand, I'm not the best at getting my thoughts out. hope it helped though!

Answer 21

hahaha, no problem, it did, thanks a lot, made a fan :P

Answer 22

haha, good! :) good luck man!

Answer 23

thanks you too :p