MHB Solve for q: Q=p-q/2 q=p-2Q

[OMGMathPLS]

Solve for q:

Q=p-q/2

Correct answer :
p-2Q
or
-2Q+pHow can this answer be either p-2Q OR -2Q+p. I mean I can see they are the same value but how would you do it to get different answers?

 

[MarkFL]

I assume you mean:

Q=(p-q)/2

or:

$$Q=\frac{p-q}{2}$$

Multiply through by $2$:

$$2Q=p-q$$

Add $q-2Q$ to both sides:

$$q=p-2Q$$

Now, let's go back to:

$$Q=\frac{p-q}{2}$$

Multiply through by $-2$:

$$-2Q=q-p$$

Add $p$ to both sides:

$$-2Q+p=q$$

The form you get (assuming you use valid operations), and/or choose to use depends largely on you. The commutative law of addition results in:

$$p-2Q=-2Q+p$$

Personally, I avoid the use of leading negatives whenever possible. :D

 

[OMGMathPLS]

Thanks.Why did you add q-2Q to both sides?

 

[MarkFL]

Thanks.Why did you add q-2Q to both sides?

Doing so resulted in the left side of the equation having just $q$ in it, which is what we want, as we are solving for $q$.. :D

 

[ineedhelpnow]

Q=(p-q)/2
multiply both sides by 2 and the 2 on the right hand side cancels out

2Q=p-q
2Q-p=-q

you don't want to have -q so instead you want to end up with something for q. just flip the signs or multiply the whole thing by -.

-(2Q-p=-q)
-2Q+p=q

p-2Q is the same as p+(-2Q) and that's equivalent to -2Q+p in which both cases the the 2Q has a negative sign and the p has a positive.

hope that help!