Question

How do you solve `at+b=ar-c` for a?

Answer 1

combine the a terms on one side and all the other terms on the other to get to `-(c+b)/(t-r)`

Explanation:

Start with the original:

`at+b=ar-c`

Let's combine the terms with `a` on the left side and everything else on the right, so we'll subtract `ar` from both sides and subtract b from both sides:

`at-ar=-c-b`

We can now factor out a:

`a(t-r)=-c-b`

And now divide by (t-r) to solve for a:

`a=(-c-b)/(t-r)=((-(c+b))/(t-r))=-(c+b)/(t-r)`