Solve for a a(4-x)=-3x+b

$a (4 - x) = - 3 x + b$

Divide each term in $a (4 - x) = - 3 x + b$ by $4 - x$ .

$\frac{a (4 - x)}{4 - x} = \frac{- 3 x}{4 - x} + \frac{b}{4 - x}$

Simplify the left side.

Cancel the common factor of $4 - x$ .

Cancel the common factor.

$\frac{a (4 - x)}{4 - x} = \frac{- 3 x}{4 - x} + \frac{b}{4 - x}$

Divide $a$ by $1$ .

$a = \frac{- 3 x}{4 - x} + \frac{b}{4 - x}$

Simplify the right side.

Move the negative in front of the fraction.

$a = - \frac{3 x}{4 - x} + \frac{b}{4 - x}$

Simplify terms.

Combine the numerators over the common denominator.

$a = \frac{- 3 x + b}{4 - x}$

Factor $- 1$ out of $- 3 x$ .

$a = \frac{- (3 x) + b}{4 - x}$

Factor $- 1$ out of $b$ .

$a = \frac{- (3 x) - 1 (- b)}{4 - x}$

Factor $- 1$ out of $- (3 x) - 1 (- b)$ .

$a = \frac{- (3 x - b)}{4 - x}$

Simplify the expression.

Rewrite $- (3 x - b)$ as $- 1 (3 x - b)$ .

$a = \frac{- 1 (3 x - b)}{4 - x}$

Move the negative in front of the fraction.

$a = - \frac{3 x - b}{4 - x}$