Solve for x ax+b=cx+d

$a x + b = c x + d$

Step 1

Subtract $c x$ from both sides of the equation.

$a x + b - c x = d$

Step 2

Subtract $b$ from both sides of the equation.

$a x - c x = d - b$

Step 3

Factor $x$ out of $a x - c x$ .

Factor $x$ out of $a x$ .

$x a - c x = d - b$

Factor $x$ out of $- c x$ .

$x a + x (- c) = d - b$

Factor $x$ out of $x a + x (- c)$ .

$x (a - c) = d - b$

Step 4

Divide each term in $x (a - c) = d - b$ by $a - c$ and simplify.

Divide each term in $x (a - c) = d - b$ by $a - c$ .

$\frac{x (a - c)}{a - c} = \frac{d}{a - c} + \frac{- b}{a - c}$

Simplify the left side.

Cancel the common factor of $a - c$ .

Cancel the common factor.

$\frac{x (a - c)}{a - c} = \frac{d}{a - c} + \frac{- b}{a - c}$

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{d}{a - c} - \frac{b}{a - c}$

Combine the numerators over the common denominator.

$x = \frac{d - b}{a - c}$