Solve 2/3(9x+6)-1/2(8x-4)

$$\frac{ 2 }{ 3 } (9x+6)- \frac{ 1 }{ 2 } (8x-4)$$

Evaluate

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

Solution Steps

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

$$\frac{2}{3}\times 9x+\frac{2}{3}\times 6-\frac{1}{2}\left(8x-4\right)$$

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

$$\frac{2\times 9}{3}x+\frac{2}{3}\times 6-\frac{1}{2}\left(8x-4\right)$$

Multiply 2 and 9 to get 18.

$$\frac{18}{3}x+\frac{2}{3}\times 6-\frac{1}{2}\left(8x-4\right)$$

Divide 18 by 3 to get 6.

$$6x+\frac{2}{3}\times 6-\frac{1}{2}\left(8x-4\right)$$

Express \frac{2}{3}\times 6 as a single fraction.

$$6x+\frac{2\times 6}{3}-\frac{1}{2}\left(8x-4\right)$$

Multiply 2 and 6 to get 12.

$$6x+\frac{12}{3}-\frac{1}{2}\left(8x-4\right)$$

Divide 12 by 3 to get 4.

$$6x+4-\frac{1}{2}\left(8x-4\right)$$

Use the distributive property to multiply -\frac{1}{2} by 8x-4.

$$6x+4-\frac{1}{2}\times 8x-\frac{1}{2}\left(-4\right)$$

Express -\frac{1}{2}\times 8 as a single fraction.

$$6x+4+\frac{-8}{2}x-\frac{1}{2}\left(-4\right)$$

Divide -8 by 2 to get -4.

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

Express -\frac{1}{2}\left(-4\right) as a single fraction.

$$6x+4-4x+\frac{-\left(-4\right)}{2}$$

Multiply -1 and -4 to get 4.

$$6x+4-4x+\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$6x+4-4x+2$$

Combine 6x and -4x to get 2x.

$$2x+4+2$$

Add 4 and 2 to get 6.

$$2x+6$$

Expand

$$2x+6$$

Solution Steps

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

$$\frac{2}{3}\times 9x+\frac{2}{3}\times 6-\frac{1}{2}\left(8x-4\right)$$

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

$$\frac{2\times 9}{3}x+\frac{2}{3}\times 6-\frac{1}{2}\left(8x-4\right)$$

Multiply 2 and 9 to get 18.

$$\frac{18}{3}x+\frac{2}{3}\times 6-\frac{1}{2}\left(8x-4\right)$$

Divide 18 by 3 to get 6.

$$6x+\frac{2}{3}\times 6-\frac{1}{2}\left(8x-4\right)$$

Express \frac{2}{3}\times 6 as a single fraction.

$$6x+\frac{2\times 6}{3}-\frac{1}{2}\left(8x-4\right)$$

Multiply 2 and 6 to get 12.

$$6x+\frac{12}{3}-\frac{1}{2}\left(8x-4\right)$$

Divide 12 by 3 to get 4.

$$6x+4-\frac{1}{2}\left(8x-4\right)$$

Use the distributive property to multiply -\frac{1}{2} by 8x-4.

$$6x+4-\frac{1}{2}\times 8x-\frac{1}{2}\left(-4\right)$$

Express -\frac{1}{2}\times 8 as a single fraction.

$$6x+4+\frac{-8}{2}x-\frac{1}{2}\left(-4\right)$$

Divide -8 by 2 to get -4.

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

Express -\frac{1}{2}\left(-4\right) as a single fraction.

$$6x+4-4x+\frac{-\left(-4\right)}{2}$$

Multiply -1 and -4 to get 4.

$$6x+4-4x+\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$6x+4-4x+2$$

Combine 6x and -4x to get 2x.

$$2x+4+2$$

Add 4 and 2 to get 6.

$$2x+6$$