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

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

Solve for x

$$x<\frac{1}{3}$$

Solution Steps

Use the distributive property to multiply 4 by 2x-1.

$$8x-4<2\left(x-1\right)$$

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

$$8x-4<2x-2$$

Subtract 2x from both sides.

$$8x-4-2x<-2$$

Combine 8x and -2x to get 6x.

$$6x-4<-2$$

Add 4 to both sides.

$$6x<-2+4$$

Add -2 and 4 to get 2.

$$6x<2$$

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$x<\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$x<\frac{1}{3}$$