Solve 2x-1/3<x-1/2

$$\frac { 2 x - 1 } { 3 } < \frac { x - 1 } { 2 }$$

Solve for x

$$x<-1$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(2x-1\right)<3\left(x-1\right)$$

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

$$4x-2<3\left(x-1\right)$$

Use the distributive property to multiply 3 by x-1.

$$4x-2<3x-3$$

Subtract 3x from both sides.

$$4x-2-3x<-3$$

Combine 4x and -3x to get x.

$$x-2<-3$$

Add 2 to both sides.

$$x<-3+2$$

Add -3 and 2 to get -1.

$$x<-1$$