Solve 4(2/3x-3)>8

$$4 ( \frac { 2 } { 3 } x - 3 ) > 8$$

Solve for x

$$x>\frac{15}{2}$$

Solution Steps

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$\frac{2}{3}x-3>\frac{8}{4}$$

Divide 8 by 4 to get 2.

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

Add 3 to both sides.

$$\frac{2}{3}x>2+3$$

Add 2 and 3 to get 5.

$$\frac{2}{3}x>5$$

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.

$$x>5\times \frac{3}{2}$$

Express 5\times \frac{3}{2} as a single fraction.

$$x>\frac{5\times 3}{2}$$

Multiply 5 and 3 to get 15.

$$x>\frac{15}{2}$$