Solve 1.6-0.3/2y+4.4+1.5/5y<-4.05y

$$\frac{ 1.6-0.3 }{ 2 } y+ \frac{ 4.4+1.5 }{ 5 } y < -4.05y$$

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.

$$y<0$$