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

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

Solve for x

$$x<-\frac{11}{5}$$

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.

$$9\left(x+1\right)<2\left(2x+2\right)-6$$

Use the distributive property to multiply 9 by x+1.

$$9x+9<2\left(2x+2\right)-6$$

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

$$9x+9<4x+4-6$$

Subtract 6 from 4 to get -2.

$$9x+9<4x-2$$

Subtract 4x from both sides.

$$9x+9-4x<-2$$

Combine 9x and -4x to get 5x.

$$5x+9<-2$$

Subtract 9 from both sides.

$$5x<-2-9$$

Subtract 9 from -2 to get -11.

$$5x<-11$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x<-\frac{11}{5}$$