Solve 2x-b/x-1=3

$$\frac { 2 x - b } { x - 1 } = 3$$

Solve for b

$$b=3-x$$

$$x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-1.

$$2x-b=3\left(x-1\right)$$

Use the distributive property to multiply 3 by x-1.

$$2x-b=3x-3$$

Subtract 2x from both sides.

$$-b=3x-3-2x$$

Combine 3x and -2x to get x.

$$-b=x-3$$

Divide both sides by -1.

$$\frac{-b}{-1}=\frac{x-3}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$b=\frac{x-3}{-1}$$

Divide x-3 by -1.

$$b=3-x$$

Solve for x

$$x=3-b$$

$$b\neq 2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

$$2x-b=3\left(x-1\right)$$

Use the distributive property to multiply 3 by x-1.

$$2x-b=3x-3$$

Subtract 3x from both sides.

$$2x-b-3x=-3$$

Combine 2x and -3x to get -x.

$$-x-b=-3$$

Add b to both sides.

$$-x=-3+b$$

The equation is in standard form.

$$-x=b-3$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{b-3}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{b-3}{-1}$$

Divide -3+b by -1.

$$x=3-b$$

Variable x cannot be equal to 1.

$$x=3-b\text{, }x\neq 1$$