# Check my arithmetic for this formula.

I have this formula: F = qVe + (Pe - Pa) * Ae; I want to get q by its self. This what I did to get q by its self.

F = qVe + (Pe - Pa) * Ae

$$\frac{F - (P_e - P_a)}{(A_e)} = \frac{(V_e * q)(A_e)}{(A_e)}$$

[( F - (Pe - Pa)) ÷ Ae] ÷ Ve = q

This is how I got q by its self in order to solve for q. I'm not sure if its correct, so please look over it to see if its correct. Thank you for your time.

Office_Shredder
Staff Emeritus
Gold Member
It's wrong. When you move the (Pe-Pa)Ae term over to the side with F, you lost the Ae and multiplied Veq by Ae instead.

...you lost the Ae and multiplied Veq by Ae instead.
I don't get what you are saying by loosing Ae from (Pe - Pa). I get wat you are saying after the and part of the sentence. Can you change the place of Ae because of order of operations, you will have to multiply first before you can add: + Ae * (Pe - Pa)?

Nabeshin
I think what you did, correct me if I'm wrong, is subtract (Pe-Pa) from both sides and then divide everything by Ae.

The problem with this is that subtracting from the right hand side doesn't eliminate the (Pe-Pa) because it has an Ae attached to it. What Office_Shredder is saying is you have to move the entire term, Ae(Pe-P), over to the other side:

$$F=qV_{e}+(P_{e}-P_{a})A_{e}$$

Subtract $$(P_{e}-P_{a})A_{e}$$ from both sides:

$$F-(P_{e}-P_{a})A_{e}=qV_{e}+(P_{e}-P_{a})A_{e}-(P_{e}-P_{a})A_{e}$$

$$F-(P_{e}-P_{a})A_{e}=qV_{e}$$

$$\frac{F-(P_{e}-P_{a})A_{e}}{V_{e}}=q$$

To make explicit what you did:

$$F=qV_{e}+(P_{e}-P_{a})A_{e}$$

$$F-(P_{e}-P_{a})=qV_{e}+(P_{e}-P_{a})A_{e}-(P_{e}-P_{a})$$

And you see the terms don't drop out on the right hand side. Hope this clarifies.

Ok, yes it does clarify. Ae is meant to multiply with (Pe - Pa) not to divide F - (Pe - Pa), which is not dividing but multiplying. Thank you for your help.