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

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

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.

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

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

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

Add 3 and 6 to get 9.

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

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

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

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.

$$x>1$$