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

May 29, 2016

combine the a terms on one side and all the other terms on the other to get to $- \frac{c + b}{t - r}$

#### Explanation:

$a t + b = a r - c$

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

$a t - a r = - c - b$

We can now factor out a:

$a \left(t - r\right) = - c - b$

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

$a = \frac{- c - b}{t - r} = \left(\frac{- \left(c + b\right)}{t - r}\right) = - \frac{c + b}{t - r}$