Solve for x 2ax-b=cx+d

$2 a x - b = c x + d$

Step 1

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

$2 a x - b - c x = d$

Step 2

Add $b$ to both sides of the equation.

$2 a x - c x = d + b$

Step 3

Factor $x$ out of $2 a x - c x$ .

Factor $x$ out of $2 a x$ .

$x (2 a) - c x = d + b$

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

$x (2 a) + x (- c) = d + b$

Factor $x$ out of $x (2 a) + x (- c)$ .

$x (2 a - c) = d + b$

Step 4

Divide each term in $x (2 a - c) = d + b$ by $2 a - c$ and simplify.

Divide each term in $x (2 a - c) = d + b$ by $2 a - c$ .

$\frac{x (2 a - c)}{2 a - c} = \frac{d}{2 a - c} + \frac{b}{2 a - c}$

Simplify the left side.

Cancel the common factor of $2 a - c$ .

Cancel the common factor.

$\frac{x (2 a - c)}{2 a - c} = \frac{d}{2 a - c} + \frac{b}{2 a - c}$

Divide $x$ by $1$ .

$x = \frac{d}{2 a - c} + \frac{b}{2 a - c}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{d + b}{2 a - c}$