Solve x-1/3>x-3

$$\frac { x - 1 } { 3 } > x - 3$$

Solve for x

$$x<4$$

Solution Steps

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$x-1>3x-9$$

Subtract 3x from both sides.

$$x-1-3x>-9$$

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

$$-2x-1>-9$$

Add 1 to both sides.

$$-2x>-9+1$$

Add -9 and 1 to get -8.

$$-2x>-8$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x<\frac{-8}{-2}$$

Divide -8 by -2 to get 4.

$$x<4$$