Solve 1,6-0,3/2y+4,4+1,5/5y<-4,05y

$$\frac { 1,6 - 0,3 } { 2 } y + \frac { 4,4 + 1,5 } { 5 } y < - 4,05 y$$

Solve for y

$$y<0$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 2;5. Since 10 is positive, the inequality direction remains the same.

$$5\left(1,6-0,3\right)y+2\left(4,4+1,5\right)y<-40,5y$$

Subtract 0,3 from 1,6 to get 1,3.

$$5\times 1,3y+2\left(4,4+1,5\right)y<-40,5y$$

Multiply 5 and 1,3 to get 6,5.

$$6,5y+2\left(4,4+1,5\right)y<-40,5y$$

Add 4,4 and 1,5 to get 5,9.

$$6,5y+2\times 5,9y<-40,5y$$

Multiply 2 and 5,9 to get 11,8.

$$6,5y+11,8y<-40,5y$$

Combine 6,5y and 11,8y to get 18,3y.

$$18,3y<-40,5y$$

Add 40,5y to both sides.

$$18,3y+40,5y<0$$

Combine 18,3y and 40,5y to get 58,8y.

$$58,8y<0$$

Product of two numbers is <0 if one is >0 and the other is <0. Since 58,8>0, y must be <0.

$$y<0$$