Solve 2/3x-7/9>-2

$$\frac { 2 } { 3 } x - \frac { 7 } { 9 } > - 2$$

Solve for x

$$x>-\frac{11}{6}$$

Solution Steps

Add \frac{7}{9} to both sides.

$$\frac{2}{3}x>-2+\frac{7}{9}$$

Convert -2 to fraction -\frac{18}{9}.

$$\frac{2}{3}x>-\frac{18}{9}+\frac{7}{9}$$

Since -\frac{18}{9} and \frac{7}{9} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}x>\frac{-18+7}{9}$$

Add -18 and 7 to get -11.

$$\frac{2}{3}x>-\frac{11}{9}$$

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.

$$x>-\frac{11}{9}\times \frac{3}{2}$$

Multiply -\frac{11}{9} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{-11\times 3}{9\times 2}$$

Do the multiplications in the fraction \frac{-11\times 3}{9\times 2}.

$$x>\frac{-33}{18}$$

Reduce the fraction \frac{-33}{18} to lowest terms by extracting and canceling out 3.

$$x>-\frac{11}{6}$$