Solve 4/3(-x+2)-x+4/6>x/2+2

$$\frac { 4 } { 3 } ( - x + 2 ) - \frac { x + 4 } { 6 } > \frac { x } { 2 } + 2$$

Solve for x

$$x<0$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,6,2. Since 6 is positive, the inequality direction remains the same.

$$8\left(-x+2\right)-\left(x+4\right)>3x+12$$

Use the distributive property to multiply 8 by -x+2.

$$8\left(-x\right)+16-\left(x+4\right)>3x+12$$

To find the opposite of x+4, find the opposite of each term.

$$8\left(-x\right)+16-x-4>3x+12$$

Subtract 4 from 16 to get 12.

$$8\left(-x\right)+12-x>3x+12$$

Subtract 3x from both sides.

$$8\left(-x\right)+12-x-3x>12$$

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

$$8\left(-x\right)+12-4x>12$$

Subtract 12 from both sides.

$$8\left(-x\right)-4x>12-12$$

Subtract 12 from 12 to get 0.

$$8\left(-x\right)-4x>0$$

Multiply 8 and -1 to get -8.

$$-8x-4x>0$$

Combine -8x and -4x to get -12x.

$$-12x>0$$

Product of two numbers is >0 if both are >0 or both are <0. Since -12<0, x must be <0.

$$x<0$$