Solve 3-x>2(x-1)

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

Solve for x

$$x<\frac{5}{3}$$

Solution Steps

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

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

Subtract 2x from both sides.

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

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

$$3-3x>-2$$

Subtract 3 from both sides.

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

Subtract 3 from -2 to get -5.

$$-3x>-5$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x<\frac{-5}{-3}$$

Fraction \frac{-5}{-3} can be simplified to \frac{5}{3} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{5}{3}$$