Express p in terms of the other quantities

[James10492]

Hi all, I am having some difficulties with the following problem and would be much relieved if anyone could help.

Given (P- 1/2 Q) = b(Q - 1/2 P), rearrange the terms so as to express P in terms of the other quantities.

To start I wrote the terms as they would be after the operations inside the brackets

(2P-Q/2) = b(2Q-P/2)

then

2P-Q/2 = 2bQ - bP/2

so I think now you can multiply both sides by two to make

2P-Q = 2bQ - bP

and then

2P-Q/b = 2Q-P

so

P = 2Q - 2P-Q/b

which resembles nothing that is in the answer key. What am I failing to see?

 

[Deleted member 4993]

Hi all, I am having some difficulties with the following problem and would be much relieved if anyone could help.

Given (P- 1/2 Q) = b(Q - 1/2 P), rearrange the terms so as to express P in terms of the other quantities.
To start I wrote the terms as they would be after the operations inside the brackets
(2P-Q/2) = b(2Q-P/2)
then
2P-Q/2 = 2bQ - bP/2
so I think now you can multiply both sides by two to make
2P-Q = 2bQ - bP
and then
2P-Q/b = 2Q-P
so
P = 2Q - 2P-Q/b

which resembles nothing that is in the answer key. What am I failing to see?

You said:

2P-Q/2 = 2bQ - bP/2
so I think now you can multiply both sides by two to make
2P-Q = 2bQ - bP ....................................this is incorrect

It should be:

2*2 *P - Q/2 * 2 = 2*2 * b * Q - b*P/2 *2

giving you

4P - Q = 4bQ - bP

continue.......

 

[James10492]

You said:

2P-Q/2 = 2bQ - bP/2
so I think now you can multiply both sides by two to make
2P-Q = 2bQ - bP ....................................this is incorrect

It should be:

2*2 *P - Q/2 * 2 = 2*2 * b * Q - b*P/2 *2

giving you

4P - Q = 4bQ - bP

continue.......

How did you get 4P - Q = 4bQ - bP, and not 4P - 2Q = 4bQ - 2bP? 2P-Q and 2Q-P are unit terms so everything should be multiplied by two no?

 

[Dr.Peterson]

Let's focus on the first thing you did:

Given (P- 1/2 Q) = b(Q - 1/2 P), rearrange the terms so as to express P in terms of the other quantities.

To start I wrote the terms as they would be after the operations inside the brackets

(2P-Q/2) = b(2Q-P/2)

Can you explain your thinking here?

The left-hand side in the original is P - 1/2 Q; the brackets do nothing and the only operations are multiplication by 1/2, and subtraction. The 1/2 Q is the same as Q/2, so it can be rewritten as P - Q/2.

But how did you change P to 2P? There is something you are thinking here that has to be corrected, and I'll need your explanation in order to know what it is. You did the same thing on the right-hand side.

 

[Steven G]

2P-Q/2 = 2bQ - bP/2 so I think now you can multiply both sides by two to make 2P-Q = 2bQ - bP

The problem here is that you did NOT multiply both sides by two. You multiplied PART of each side by two which doesn't work.

For example, 5 + 1/2 = 5 1/2 and 3 + 5/2 = 5 1/2 as well.

So 5 + 1/2 = 3 + 5/2 BUT 5 + 2*1/2 = 5+1 = 6 while 3 + 2*(5/2) = 3 + 5 = 8. NOTE that 6 does not equal 8.