Solve [2x-2]<[4x-5]

$$[ 2 x - 2 ] < [ 4 x - 5 ]$$

Solve for x

$$x>\frac{3}{2}$$

Solution Steps

Subtract 4x from both sides.

$$2x-2-4x<-5$$

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

$$-2x-2<-5$$

Add 2 to both sides.

$$-2x<-5+2$$

Add -5 and 2 to get -3.

$$-2x<-3$$

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

$$x>\frac{-3}{-2}$$

Fraction \frac{-3}{-2} can be simplified to \frac{3}{2} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{3}{2}$$