Solve 5(x-1)+3x<2x-1=

$$5(x-1)+3x < 2x-1=$$

Solve for x

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

Solution Steps

Use the distributive property to multiply 5 by x-1.

$$5x-5+3x<2x-1$$

Combine 5x and 3x to get 8x.

$$8x-5<2x-1$$

Subtract 2x from both sides.

$$8x-5-2x<-1$$

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

$$6x-5<-1$$

Add 5 to both sides.

$$6x<-1+5$$

Add -1 and 5 to get 4.

$$6x<4$$

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

$$x<\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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