Solve 1/32/3x>6x-3/2

$$\frac { 1 } { 3 } \frac { 2 } { 3 } x > \frac { 6 x - 3 } { 2 }$$

Solve for x

$$x<\frac{27}{50}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\times \frac{2}{3}x>3\left(6x-3\right)$$

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

$$\frac{2\times 2}{3}x>3\left(6x-3\right)$$

Multiply 2 and 2 to get 4.

$$\frac{4}{3}x>3\left(6x-3\right)$$

Use the distributive property to multiply 3 by 6x-3.

$$\frac{4}{3}x>18x-9$$

Subtract 18x from both sides.

$$\frac{4}{3}x-18x>-9$$

Combine \frac{4}{3}x and -18x to get -\frac{50}{3}x.

$$-\frac{50}{3}x>-9$$

Multiply both sides by -\frac{3}{50}, the reciprocal of -\frac{50}{3}. Since -\frac{50}{3} is negative, the inequality direction is changed.

$$x<-9\left(-\frac{3}{50}\right)$$

Express -9\left(-\frac{3}{50}\right) as a single fraction.

$$x<\frac{-9\left(-3\right)}{50}$$

Multiply -9 and -3 to get 27.

$$x<\frac{27}{50}$$