Solve 5+2x/3-x+2/2>x+5/4

$$\frac { 5 + 2 x } { 3 } - \frac { x + 2 } { 2 } > \frac { x + 5 } { 4 }$$

Solve for x

$$x<-7$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,2,4. Since 12 is positive, the inequality direction remains the same.

$$4\left(5+2x\right)-6\left(x+2\right)>3\left(x+5\right)$$

Use the distributive property to multiply 4 by 5+2x.

$$20+8x-6\left(x+2\right)>3\left(x+5\right)$$

Use the distributive property to multiply -6 by x+2.

$$20+8x-6x-12>3\left(x+5\right)$$

Combine 8x and -6x to get 2x.

$$20+2x-12>3\left(x+5\right)$$

Subtract 12 from 20 to get 8.

$$8+2x>3\left(x+5\right)$$

Use the distributive property to multiply 3 by x+5.

$$8+2x>3x+15$$

Subtract 3x from both sides.

$$8+2x-3x>15$$

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

$$8-x>15$$

Subtract 8 from both sides.

$$-x>15-8$$

Subtract 8 from 15 to get 7.

$$-x>7$$

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

$$x<-7$$