Solve 5x-1/3-(12-2x/3)>0

$$5 x - \frac { 1 } { 3 } - ( 12 - \frac { 2 x } { 3 } ) > 0$$

Solve for x

$$x>\frac{37}{17}$$

Solution Steps

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$3\left(5x-\frac{1}{3}\right)-3\left(12-\frac{2x}{3}\right)>0$$

Use the distributive property to multiply 3 by 5x-\frac{1}{3}.

$$15x+3\left(-\frac{1}{3}\right)-3\left(12-\frac{2x}{3}\right)>0$$

Cancel out 3 and 3.

$$15x-1-3\left(12-\frac{2x}{3}\right)>0$$

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$3\left(15x-1\right)-9\left(12-\frac{2x}{3}\right)>0$$

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$9\left(15x-1\right)-3\times 9\left(12-\frac{2x}{3}\right)>0$$

Use the distributive property to multiply 9 by 15x-1.

$$135x-9-3\times 9\left(12-\frac{2x}{3}\right)>0$$

Multiply -3 and 9 to get -27.

$$135x-9-27\left(12-\frac{2x}{3}\right)>0$$

Use the distributive property to multiply -27 by 12-\frac{2x}{3}.

$$135x-9-324+27\times \frac{2x}{3}>0$$

Cancel out 3, the greatest common factor in 27 and 3.

$$135x-9-324+9\times 2x>0$$

Multiply 9 and 2 to get 18.

$$135x-9-324+18x>0$$

Subtract 324 from -9 to get -333.

$$135x-333+18x>0$$

Combine 135x and 18x to get 153x.

$$153x-333>0$$

Add 333 to both sides. Anything plus zero gives itself.

$$153x>333$$

Divide both sides by 153. Since 153 is positive, the inequality direction remains the same.

$$x>\frac{333}{153}$$

Reduce the fraction \frac{333}{153} to lowest terms by extracting and canceling out 9.

$$x>\frac{37}{17}$$