Solve 2/9<2/3y

$$\frac { 2 } { 9 } < \frac { 2 } { 3 } y$$

Solve for y

$$y>\frac{1}{3}$$

Solution Steps

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}. Since \frac{2}{3} is positive, the inequality direction remains the same.

$$\frac{2}{9}\times \frac{3}{2}<y$$

Multiply \frac{2}{9} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 3}{9\times 2}<y$$

Cancel out 2 in both numerator and denominator.

$$\frac{3}{9}<y$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{1}{3}<y$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$y>\frac{1}{3}$$