Solve x(3-2b)-1=x(2-3b-b)

$$x ( 3 - 2 b ) - 1 = x ( 2 - 3 b - b )$$

Solve for b

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

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 3-2b.

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

Combine -3b and -b to get -4b.

$$3x-2xb-1=x\left(2-4b\right)$$

Use the distributive property to multiply x by 2-4b.

$$3x-2xb-1=2x-4xb$$

Add 4xb to both sides.

$$3x-2xb-1+4xb=2x$$

Combine -2xb and 4xb to get 2xb.

$$3x+2xb-1=2x$$

Subtract 3x from both sides.

$$2xb-1=2x-3x$$

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

$$2xb-1=-x$$

Add 1 to both sides.

$$2xb=-x+1$$

The equation is in standard form.

$$2xb=1-x$$

Divide both sides by 2x.

$$\frac{2xb}{2x}=\frac{1-x}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

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

Divide -x+1 by 2x.

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

Solve for x

$$x=\frac{1}{2b+1}$$

$$b\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 3-2b.

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

Combine -3b and -b to get -4b.

$$3x-2xb-1=x\left(2-4b\right)$$

Use the distributive property to multiply x by 2-4b.

$$3x-2xb-1=2x-4xb$$

Subtract 2x from both sides.

$$3x-2xb-1-2x=-4xb$$

Combine 3x and -2x to get x.

$$x-2xb-1=-4xb$$

Add 4xb to both sides.

$$x-2xb-1+4xb=0$$

Combine -2xb and 4xb to get 2xb.

$$x+2xb-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$x+2xb=1$$

Combine all terms containing x.

$$\left(1+2b\right)x=1$$

The equation is in standard form.

$$\left(2b+1\right)x=1$$

Divide both sides by 1+2b.

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

Dividing by 1+2b undoes the multiplication by 1+2b.

$$x=\frac{1}{2b+1}$$