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

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

Solve for x

$$x<-1$$

Solution Steps

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

$$3\left(x-1\right)-2\left(x+1\right)<-6$$

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

$$3x-3-2\left(x+1\right)<-6$$

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

$$3x-3-2x-2<-6$$

Combine 3x and -2x to get x.

$$x-3-2<-6$$

Subtract 2 from -3 to get -5.

$$x-5<-6$$

Add 5 to both sides.

$$x<-6+5$$

Add -6 and 5 to get -1.

$$x<-1$$