Solve -4/9+2/3+2a>0

$$- \frac { 4 } { 9 } + \frac { 2 } { 3 } + 2 a > 0$$

Solve for a

$$a>-\frac{1}{9}$$

Solution Steps

Least common multiple of 9 and 3 is 9. Convert -\frac{4}{9} and \frac{2}{3} to fractions with denominator 9.

$$-\frac{4}{9}+\frac{6}{9}+2a>0$$

Since -\frac{4}{9} and \frac{6}{9} have the same denominator, add them by adding their numerators.

$$\frac{-4+6}{9}+2a>0$$

Add -4 and 6 to get 2.

$$\frac{2}{9}+2a>0$$

Subtract \frac{2}{9} from both sides. Anything subtracted from zero gives its negation.

$$2a>-\frac{2}{9}$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$a>\frac{-\frac{2}{9}}{2}$$

Express \frac{-\frac{2}{9}}{2} as a single fraction.

$$a>\frac{-2}{9\times 2}$$

Multiply 9 and 2 to get 18.

$$a>\frac{-2}{18}$$

Reduce the fraction \frac{-2}{18} to lowest terms by extracting and canceling out 2.

$$a>-\frac{1}{9}$$