Solve 2(x-1)-c=2(x-b)/b

$$2 ( x - 1 ) - c = \frac { 2 ( x - b ) } { b }$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{2x}{c-2x}\text{, }&x\neq 0\text{ and }x\neq \frac{c}{2}\\b\neq 0\text{, }&x=0\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b.

$$2\left(x-1\right)b-cb=2\left(x-b\right)$$

Use the distributive property to multiply 2 by x-1.

$$\left(2x-2\right)b-cb=2\left(x-b\right)$$

Use the distributive property to multiply 2x-2 by b.

$$2xb-2b-cb=2\left(x-b\right)$$

Use the distributive property to multiply 2 by x-b.

$$2xb-2b-cb=2x-2b$$

Add 2b to both sides.

$$2xb-2b-cb+2b=2x$$

Combine -2b and 2b to get 0.

$$2xb-cb=2x$$

Combine all terms containing b.

$$\left(2x-c\right)b=2x$$

Divide both sides by 2x-c.

$$\frac{\left(2x-c\right)b}{2x-c}=\frac{2x}{2x-c}$$

Dividing by 2x-c undoes the multiplication by 2x-c.

$$b=\frac{2x}{2x-c}$$

Variable b cannot be equal to 0.

$$b=\frac{2x}{2x-c}\text{, }b\neq 0$$

Solve for c

$$c=\frac{2x\left(b-1\right)}{b}$$

$$b\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by b.

$$2\left(x-1\right)b-cb=2\left(x-b\right)$$

Use the distributive property to multiply 2 by x-1.

$$\left(2x-2\right)b-cb=2\left(x-b\right)$$

Use the distributive property to multiply 2x-2 by b.

$$2xb-2b-cb=2\left(x-b\right)$$

Use the distributive property to multiply 2 by x-b.

$$2xb-2b-cb=2x-2b$$

Subtract 2xb from both sides.

$$-2b-cb=2x-2b-2xb$$

Add 2b to both sides.

$$-cb=2x-2b-2xb+2b$$

Combine -2b and 2b to get 0.

$$-cb=2x-2xb$$

The equation is in standard form.

$$\left(-b\right)c=2x-2bx$$

Divide both sides by -b.

$$\frac{\left(-b\right)c}{-b}=\frac{2x-2bx}{-b}$$

Dividing by -b undoes the multiplication by -b.

$$c=\frac{2x-2bx}{-b}$$

Divide 2x-2xb by -b.

$$c=2x-\frac{2x}{b}$$