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

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

Solve for x

$$x<-5$$

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.

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

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

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

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

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

Add 4x to both sides.

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

Combine -3x and 4x to get x.

$$3+x<-2$$

Subtract 3 from both sides.

$$x<-2-3$$

Subtract 3 from -2 to get -5.

$$x<-5$$