Solve 18(2x/9+1/3)-12(5x/6-1/4)=

$$18 ( \frac { 2 x } { 9 } + \frac { 1 } { 3 } ) - 12 ( \frac { 5 x } { 6 } - \frac { 1 } { 4 } ) =$$

Evaluate

$$9-6x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 3 is 9. Multiply \frac{1}{3} times \frac{3}{3}.

$$18\left(\frac{2x}{9}+\frac{3}{9}\right)-12\left(\frac{5x}{6}-\frac{1}{4}\right)$$

Since \frac{2x}{9} and \frac{3}{9} have the same denominator, add them by adding their numerators.

$$18\times \frac{2x+3}{9}-12\left(\frac{5x}{6}-\frac{1}{4}\right)$$

Cancel out 9, the greatest common factor in 18 and 9.

$$2\left(2x+3\right)-12\left(\frac{5x}{6}-\frac{1}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 4 is 12. Multiply \frac{5x}{6} times \frac{2}{2}. Multiply \frac{1}{4} times \frac{3}{3}.

$$2\left(2x+3\right)-12\left(\frac{2\times 5x}{12}-\frac{3}{12}\right)$$

Since \frac{2\times 5x}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$2\left(2x+3\right)-12\times \frac{2\times 5x-3}{12}$$

Do the multiplications in 2\times 5x-3.

$$2\left(2x+3\right)-12\times \frac{10x-3}{12}$$

Cancel out 12 and 12.

$$2\left(2x+3\right)-\left(10x-3\right)$$

Use the distributive property to multiply 2 by 2x+3.

$$4x+6-\left(10x-3\right)$$

To find the opposite of 10x-3, find the opposite of each term.

$$4x+6-10x-\left(-3\right)$$

The opposite of -3 is 3.

$$4x+6-10x+3$$

Combine 4x and -10x to get -6x.

$$-6x+6+3$$

Add 6 and 3 to get 9.

$$-6x+9$$

Expand

$$9-6x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 3 is 9. Multiply \frac{1}{3} times \frac{3}{3}.

$$18\left(\frac{2x}{9}+\frac{3}{9}\right)-12\left(\frac{5x}{6}-\frac{1}{4}\right)$$

Since \frac{2x}{9} and \frac{3}{9} have the same denominator, add them by adding their numerators.

$$18\times \frac{2x+3}{9}-12\left(\frac{5x}{6}-\frac{1}{4}\right)$$

Cancel out 9, the greatest common factor in 18 and 9.

$$2\left(2x+3\right)-12\left(\frac{5x}{6}-\frac{1}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 4 is 12. Multiply \frac{5x}{6} times \frac{2}{2}. Multiply \frac{1}{4} times \frac{3}{3}.

$$2\left(2x+3\right)-12\left(\frac{2\times 5x}{12}-\frac{3}{12}\right)$$

Since \frac{2\times 5x}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$2\left(2x+3\right)-12\times \frac{2\times 5x-3}{12}$$

Do the multiplications in 2\times 5x-3.

$$2\left(2x+3\right)-12\times \frac{10x-3}{12}$$

Cancel out 12 and 12.

$$2\left(2x+3\right)-\left(10x-3\right)$$

Use the distributive property to multiply 2 by 2x+3.

$$4x+6-\left(10x-3\right)$$

To find the opposite of 10x-3, find the opposite of each term.

$$4x+6-10x-\left(-3\right)$$

The opposite of -3 is 3.

$$4x+6-10x+3$$

Combine 4x and -10x to get -6x.

$$-6x+6+3$$

Add 6 and 3 to get 9.

$$-6x+9$$