Solve for x c=(ax+by)f

$c = (a x + b y) f$

Step 1

Rewrite the equation as $(a x + b y) f = c$ .

$(a x + b y) f = c$

Step 2

Divide each term in $(a x + b y) f = c$ by $f$ and simplify.

Divide each term in $(a x + b y) f = c$ by $f$ .

$\frac{(a x + b y) f}{f} = \frac{c}{f}$

Simplify the left side.

Cancel the common factor of $f$ .

Cancel the common factor.

$\frac{(a x + b y) f}{f} = \frac{c}{f}$

Divide $a x + b y$ by $1$ .

$a x + b y = \frac{c}{f}$

Step 3

Subtract $b y$ from both sides of the equation.

$a x = \frac{c}{f} - b y$

Step 4

Divide each term in $a x = \frac{c}{f} - b y$ by $a$ and simplify.

Divide each term in $a x = \frac{c}{f} - b y$ by $a$ .

$\frac{a x}{a} = \frac{\frac{c}{f}}{a} + \frac{- b y}{a}$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a x}{a} = \frac{\frac{c}{f}}{a} + \frac{- b y}{a}$

Divide $x$ by $1$ .

$x = \frac{\frac{c}{f}}{a} + \frac{- b y}{a}$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{c}{f} \cdot \frac{1}{a} + \frac{- b y}{a}$

Multiply $\frac{c}{f}$ by $\frac{1}{a}$ .

$x = \frac{c}{f a} + \frac{- b y}{a}$

Move the negative in front of the fraction.

$x = \frac{c}{f a} - \frac{b y}{a}$