Solve 2(x-1)-x>3(x-1)-2x-5

$$2(x-1)-x > 3(x-1)-2x-5$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

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

$$2x-2-x>3\left(x-1\right)-2x-5$$

Combine 2x and -x to get x.

$$x-2>3\left(x-1\right)-2x-5$$

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

$$x-2>3x-3-2x-5$$

Combine 3x and -2x to get x.

$$x-2>x-3-5$$

Subtract 5 from -3 to get -8.

$$x-2>x-8$$

Subtract x from both sides.

$$x-2-x>-8$$

Combine x and -x to get 0.

$$-2>-8$$

This is true for any x.

$$x\in \mathrm{R}$$