# How do you solve for a in 2a - b = ac + 3b?

Apr 25, 2018

$a = \frac{4 b}{2 - c}$

#### Explanation:

$\text{collect terms in a on the left side of the equation}$
$\text{and all other terms on the right side}$

$\text{add b to both sides}$

$2 a \cancel{- b} \cancel{+ b} = a c + 3 b + b$

$\Rightarrow 2 a = a c + 4 b$

$\text{subtract "ac" from both sides}$

$2 a - a c = \cancel{a c} \cancel{- a c} + 4 b$

$\Rightarrow 2 a - a c = 4 b$

$\text{factor out the a on the left side}$

$\Rightarrow a \left(2 - c\right) = 4 b$

$\text{divide both sides by } \left(2 - c\right)$

$\frac{a \cancel{\left(2 - c\right)}}{\cancel{2 - c}} = \frac{4 b}{2 - c}$

$\Rightarrow a = \frac{4 b}{2 - c}$