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

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

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.

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

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

$$9-3x<2\left(x+2\right)$$

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

$$9-3x<2x+4$$

Subtract 2x from both sides.

$$9-3x-2x<4$$

Combine -3x and -2x to get -5x.

$$9-5x<4$$

Subtract 9 from both sides.

$$-5x<4-9$$

Subtract 9 from 4 to get -5.

$$-5x<-5$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x>\frac{-5}{-5}$$

Divide -5 by -5 to get 1.

$$x>1$$