Solve y/5-12>(y*10/9-80)div5

$$\frac { y } { 5 } - 12 > ( y \times \frac { 10 } { 9 } - 80 ) \div 5$$

Solve for y

$$y<180$$

Solution Steps

Multiply both sides of the equation by 5. Since 5 is positive, the inequality direction remains the same.

$$y-60>y\times \frac{10}{9}-80$$

Subtract y\times \frac{10}{9} from both sides.

$$y-60-y\times \frac{10}{9}>-80$$

Combine y and -y\times \frac{10}{9} to get -\frac{1}{9}y.

$$-\frac{1}{9}y-60>-80$$

Add 60 to both sides.

$$-\frac{1}{9}y>-80+60$$

Add -80 and 60 to get -20.

$$-\frac{1}{9}y>-20$$

Multiply both sides by -9, the reciprocal of -\frac{1}{9}. Since -\frac{1}{9} is negative, the inequality direction is changed.

$$y<-20\left(-9\right)$$

Multiply -20 and -9 to get 180.

$$y<180$$