Solve 2/3(11-9x)>5x

$$\frac { 2 } { 3 } ( 11 - 9 x ) > 5 x$$

Solve for x

$$x<\frac{2}{3}$$

Solution Steps

Use the distributive property to multiply \frac{2}{3} by 11-9x.

$$\frac{2}{3}\times 11+\frac{2}{3}\left(-9\right)x>5x$$

Express \frac{2}{3}\times 11 as a single fraction.

$$\frac{2\times 11}{3}+\frac{2}{3}\left(-9\right)x>5x$$

Multiply 2 and 11 to get 22.

$$\frac{22}{3}+\frac{2}{3}\left(-9\right)x>5x$$

Express \frac{2}{3}\left(-9\right) as a single fraction.

$$\frac{22}{3}+\frac{2\left(-9\right)}{3}x>5x$$

Multiply 2 and -9 to get -18.

$$\frac{22}{3}+\frac{-18}{3}x>5x$$

Divide -18 by 3 to get -6.

$$\frac{22}{3}-6x>5x$$

Subtract 5x from both sides.

$$\frac{22}{3}-6x-5x>0$$

Combine -6x and -5x to get -11x.

$$\frac{22}{3}-11x>0$$

Subtract \frac{22}{3} from both sides. Anything subtracted from zero gives its negation.

$$-11x>-\frac{22}{3}$$

Divide both sides by -11. Since -11 is negative, the inequality direction is changed.

$$x<\frac{-\frac{22}{3}}{-11}$$

Express \frac{-\frac{22}{3}}{-11} as a single fraction.

$$x<\frac{-22}{3\left(-11\right)}$$

Multiply 3 and -11 to get -33.

$$x<\frac{-22}{-33}$$

Reduce the fraction \frac{-22}{-33} to lowest terms by extracting and canceling out -11.

$$x<\frac{2}{3}$$