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

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

Solve for x

$$x<-\frac{16}{3}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,6,3. Since 12 is positive, the inequality direction remains the same.

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

Use the distributive property to multiply 3 by x+2.

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

Use the distributive property to multiply 2 by x-3.

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

Combine 3x and 2x to get 5x.

$$5x+6-6>4\left(2x+4\right)$$

Subtract 6 from 6 to get 0.

$$5x>4\left(2x+4\right)$$

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

$$5x>8x+16$$

Subtract 8x from both sides.

$$5x-8x>16$$

Combine 5x and -8x to get -3x.

$$-3x>16$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x<-\frac{16}{3}$$