Solve 4/5-1/15y<4/3

$$\frac { 4 } { 5 } - \frac { 1 } { 15 } y < \frac { 4 } { 3 }$$

Solve for y

$$y>-8$$

Solution Steps

Subtract \frac{4}{5} from both sides.

$$-\frac{1}{15}y<\frac{4}{3}-\frac{4}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{4}{3} and \frac{4}{5} to fractions with denominator 15.

$$-\frac{1}{15}y<\frac{20}{15}-\frac{12}{15}$$

Since \frac{20}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{15}y<\frac{20-12}{15}$$

Subtract 12 from 20 to get 8.

$$-\frac{1}{15}y<\frac{8}{15}$$

Multiply both sides by -15, the reciprocal of -\frac{1}{15}. Since -\frac{1}{15} is negative, the inequality direction is changed.

$$y>\frac{8}{15}\left(-15\right)$$

Express \frac{8}{15}\left(-15\right) as a single fraction.

$$y>\frac{8\left(-15\right)}{15}$$

Multiply 8 and -15 to get -120.

$$y>\frac{-120}{15}$$

Divide -120 by 15 to get -8.

$$y>-8$$