Solve 1-x+1/2>4-x/3

$$1 - \frac { x + 1 } { 2 } > \frac { 4 - x } { 3 }$$

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.

$$6-3\left(x+1\right)>2\left(4-x\right)$$

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

$$6-3x-3>2\left(4-x\right)$$

Subtract 3 from 6 to get 3.

$$3-3x>2\left(4-x\right)$$

Use the distributive property to multiply 2 by 4-x.

$$3-3x>8-2x$$

Add 2x to both sides.

$$3-3x+2x>8$$

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

$$3-x>8$$

Subtract 3 from both sides.

$$-x>8-3$$

Subtract 3 from 8 to get 5.

$$-x>5$$

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

$$x<-5$$