a=bm+ut-iz/q solve for q

Question

me and other students think you can multiply by q to the answer but our physics teacher begs to differ. I'm just curious on how you would solve this.

Answer 1

If you multiply both sides by q, you have to multiply EVERY term on the right by q.

 

That would leave you with:

 

qa = qbm + qut - iz

 

That doesn't really help you because you have q's on both sides.

 

The first thing you have to do is get the term with q by itself on one side.  To do this, subtract bm + ut from both sides:

 

a = bm + ut - iz/q

a - bm - ut = -iz/q

 

Now you want to get q in the numerator instead of the denominator.  There is more than one way to do this.  Let's do the following:

 

Take the reciprocal of both sides:

1 / (a - bm - ut) = -q / iz

 

Multiply both sides by -iz:

-iz / (a - bm - ut) = q

 

To simplify this, multiply the numerator and denominator of the left side by -1:

iz / (bm + ut - a) - q

 

Done.