Solve 4(x-1)<5(x-2)

$$4 ( x - 1 ) < 5 ( x - 2 )$$

Solve for x

$$x>6$$

Solution Steps

Use the distributive property to multiply 4 by x-1.

$$4x-4<5\left(x-2\right)$$

Use the distributive property to multiply 5 by x-2.

$$4x-4<5x-10$$

Subtract 5x from both sides.

$$4x-4-5x<-10$$

Combine 4x and -5x to get -x.

$$-x-4<-10$$

Add 4 to both sides.

$$-x<-10+4$$

Add -10 and 4 to get -6.

$$-x<-6$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>\frac{-6}{-1}$$

Fraction \frac{-6}{-1} can be simplified to 6 by removing the negative sign from both the numerator and the denominator.

$$x>6$$