rearranging forumlas

[Snow2021]

Hello.

I am having a slight issue when it comes to rearranging formulas, my books are not the best at explaining it and dont go deep enough into.

so 7p/q-9 = 8/q-13p Rearrange for q

i understand that first thing is to remove the fractions by multiplying out the q. giving

7p-9q = 8-13pq

but after this i draw a blank at what i can and can not do. any help is appreciated in explaining but if i can i would rather not be given the answer just some help explaining

at least that way i can get the answer myself and have a better understanding of how to solve these in the future

 

[Ishuda]

Hello.

I am having a slight issue when it comes to rearranging formulas, my books are not the best at explaining it and dont go deep enough into.

so 7p/q-9 = 8/q-13p Rearrange for q

i understand that first thing is to remove the fractions by multiplying out the q. giving

7p-9q = 8-13pq

but after this i draw a blank at what i can and can not do. any help is appreciated in explaining but if i can i would rather not be given the answer just some help explaining

at least that way i can get the answer myself and have a better understanding of how to solve these in the future

Now collect the q terms on one side, say the left hand side, and all the rest on the other side. See if you can factor the expression to isolate q. As an example, suppose you did that and had
q² - 12 p q = 8p + 16
I could add p² to both sides and get
q² - 12 pq + p² = p² + 8 p + 16
re-write that as
(q - 6 p)² = (p + 4)²
or
q = 6 p \(\displaystyle \pm\)(p + 4)
Or we could have just used the quadratic equation to get the same thing. However, a lot of the time things aren't that complicated to start with.

 

[Snow2021]

Thank you for this.

I literally just managed to find a piece to help me through this.

but its much appreciated to see that my working matches up with yours.