Solve (x-1)<3(x-2)

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

Solve for x

$$x>\frac{5}{2}$$

Solution Steps

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

$$x-1<3x-6$$

Subtract 3x from both sides.

$$x-1-3x<-6$$

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

$$-2x-1<-6$$

Add 1 to both sides.

$$-2x<-6+1$$

Add -6 and 1 to get -5.

$$-2x<-5$$

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

$$x>\frac{-5}{-2}$$

Fraction \frac{-5}{-2} can be simplified to \frac{5}{2} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{5}{2}$$