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

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

Solve for x

$$x<-\frac{31}{5}$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 2,3,5. Since 30 is positive, the inequality direction remains the same.

$$15\left(x+5\right)-10\left(x+2\right)<24$$

Use the distributive property to multiply 15 by x+5.

$$15x+75-10\left(x+2\right)<24$$

Use the distributive property to multiply -10 by x+2.

$$15x+75-10x-20<24$$

Combine 15x and -10x to get 5x.

$$5x+75-20<24$$

Subtract 20 from 75 to get 55.

$$5x+55<24$$

Subtract 55 from both sides.

$$5x<24-55$$

Subtract 55 from 24 to get -31.

$$5x<-31$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x<-\frac{31}{5}$$