Solve a-2(a+2b/3)+a-2b/2

$$a - 2 ( \frac { a + 2 b } { 3 } ) + \frac { a - 2 b } { 2 }$$

Evaluate

$$\frac{5a}{6}-\frac{7b}{3}$$

Short Solution Steps

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

$$a-\frac{2\left(a+2b\right)}{3}+\frac{a-2b}{2}$$

Use the distributive property to multiply 2 by a+2b.

$$a-\frac{2a+4b}{3}+\frac{a-2b}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{3}{3}.

$$\frac{3a}{3}-\frac{2a+4b}{3}+\frac{a-2b}{2}$$

Since \frac{3a}{3} and \frac{2a+4b}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3a-\left(2a+4b\right)}{3}+\frac{a-2b}{2}$$

Do the multiplications in 3a-\left(2a+4b\right).

$$\frac{3a-2a-4b}{3}+\frac{a-2b}{2}$$

Combine like terms in 3a-2a-4b.

$$\frac{a-4b}{3}+\frac{a-2b}{2}$$

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

$$\frac{2\left(a-4b\right)}{6}+\frac{3\left(a-2b\right)}{6}$$

Since \frac{2\left(a-4b\right)}{6} and \frac{3\left(a-2b\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{2\left(a-4b\right)+3\left(a-2b\right)}{6}$$

Do the multiplications in 2\left(a-4b\right)+3\left(a-2b\right).

$$\frac{2a-8b+3a-6b}{6}$$

Combine like terms in 2a-8b+3a-6b.

$$\frac{5a-14b}{6}$$

Expand

$$\frac{5a}{6}-\frac{7b}{3}$$

Short Solution Steps

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

$$a-\frac{2\left(a+2b\right)}{3}+\frac{a-2b}{2}$$

Use the distributive property to multiply 2 by a+2b.

$$a-\frac{2a+4b}{3}+\frac{a-2b}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{3}{3}.

$$\frac{3a}{3}-\frac{2a+4b}{3}+\frac{a-2b}{2}$$

Since \frac{3a}{3} and \frac{2a+4b}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3a-\left(2a+4b\right)}{3}+\frac{a-2b}{2}$$

Do the multiplications in 3a-\left(2a+4b\right).

$$\frac{3a-2a-4b}{3}+\frac{a-2b}{2}$$

Combine like terms in 3a-2a-4b.

$$\frac{a-4b}{3}+\frac{a-2b}{2}$$

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

$$\frac{2\left(a-4b\right)}{6}+\frac{3\left(a-2b\right)}{6}$$

Since \frac{2\left(a-4b\right)}{6} and \frac{3\left(a-2b\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{2\left(a-4b\right)+3\left(a-2b\right)}{6}$$

Do the multiplications in 2\left(a-4b\right)+3\left(a-2b\right).

$$\frac{2a-8b+3a-6b}{6}$$

Combine like terms in 2a-8b+3a-6b.

$$\frac{5a-14b}{6}$$