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

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

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.

$$4\left(-x+1\right)<-3\left(x+1\right)+6$$

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

$$4\left(-x\right)+4<-3\left(x+1\right)+6$$

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

$$4\left(-x\right)+4<-3x-3+6$$

Add -3 and 6 to get 3.

$$4\left(-x\right)+4<-3x+3$$

Add 3x to both sides.

$$4\left(-x\right)+4+3x<3$$

Subtract 4 from both sides.

$$4\left(-x\right)+3x<3-4$$

Subtract 4 from 3 to get -1.

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

Multiply 4 and -1 to get -4.

$$-4x+3x<-1$$

Combine -4x and 3x to get -x.

$$-x<-1$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>\frac{-1}{-1}$$

Divide -1 by -1 to get 1.

$$x>1$$