Solve 2/3(9a-6)+1/2(2a-10)

$$\frac { 2 } { 3 } ( 9 a - 6 ) + \frac { 1 } { 2 } ( 2 a - 10 )$$

Evaluate

$$7a-9$$

Solution Steps

Use the distributive property to multiply \frac{2}{3} by 9a-6.

$$\frac{2}{3}\times 9a+\frac{2}{3}\left(-6\right)+\frac{1}{2}\left(2a-10\right)$$

Express \frac{2}{3}\times 9 as a single fraction.

$$\frac{2\times 9}{3}a+\frac{2}{3}\left(-6\right)+\frac{1}{2}\left(2a-10\right)$$

Multiply 2 and 9 to get 18.

$$\frac{18}{3}a+\frac{2}{3}\left(-6\right)+\frac{1}{2}\left(2a-10\right)$$

Divide 18 by 3 to get 6.

$$6a+\frac{2}{3}\left(-6\right)+\frac{1}{2}\left(2a-10\right)$$

Express \frac{2}{3}\left(-6\right) as a single fraction.

$$6a+\frac{2\left(-6\right)}{3}+\frac{1}{2}\left(2a-10\right)$$

Multiply 2 and -6 to get -12.

$$6a+\frac{-12}{3}+\frac{1}{2}\left(2a-10\right)$$

Divide -12 by 3 to get -4.

$$6a-4+\frac{1}{2}\left(2a-10\right)$$

Use the distributive property to multiply \frac{1}{2} by 2a-10.

$$6a-4+\frac{1}{2}\times 2a+\frac{1}{2}\left(-10\right)$$

Cancel out 2 and 2.

$$6a-4+a+\frac{1}{2}\left(-10\right)$$

Multiply \frac{1}{2} and -10 to get \frac{-10}{2}.

$$6a-4+a+\frac{-10}{2}$$

Divide -10 by 2 to get -5.

$$6a-4+a-5$$

Combine 6a and a to get 7a.

$$7a-4-5$$

Subtract 5 from -4 to get -9.

$$7a-9$$

Expand

$$7a-9$$

Solution Steps

Use the distributive property to multiply \frac{2}{3} by 9a-6.

$$\frac{2}{3}\times 9a+\frac{2}{3}\left(-6\right)+\frac{1}{2}\left(2a-10\right)$$

Express \frac{2}{3}\times 9 as a single fraction.

$$\frac{2\times 9}{3}a+\frac{2}{3}\left(-6\right)+\frac{1}{2}\left(2a-10\right)$$

Multiply 2 and 9 to get 18.

$$\frac{18}{3}a+\frac{2}{3}\left(-6\right)+\frac{1}{2}\left(2a-10\right)$$

Divide 18 by 3 to get 6.

$$6a+\frac{2}{3}\left(-6\right)+\frac{1}{2}\left(2a-10\right)$$

Express \frac{2}{3}\left(-6\right) as a single fraction.

$$6a+\frac{2\left(-6\right)}{3}+\frac{1}{2}\left(2a-10\right)$$

Multiply 2 and -6 to get -12.

$$6a+\frac{-12}{3}+\frac{1}{2}\left(2a-10\right)$$

Divide -12 by 3 to get -4.

$$6a-4+\frac{1}{2}\left(2a-10\right)$$

Use the distributive property to multiply \frac{1}{2} by 2a-10.

$$6a-4+\frac{1}{2}\times 2a+\frac{1}{2}\left(-10\right)$$

Cancel out 2 and 2.

$$6a-4+a+\frac{1}{2}\left(-10\right)$$

Multiply \frac{1}{2} and -10 to get \frac{-10}{2}.

$$6a-4+a+\frac{-10}{2}$$

Divide -10 by 2 to get -5.

$$6a-4+a-5$$

Combine 6a and a to get 7a.

$$7a-4-5$$

Subtract 5 from -4 to get -9.

$$7a-9$$