Solve 1/2[14x-2/3(9x-21y)-2(x+y)]

$$\frac { 1 } { 2 } [ 14 x - \frac { 2 } { 3 } ( 9 x - 21 y ) - 2 ( x + y ) ]$$

Evaluate

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

Solution Steps

Use the distributive property to multiply -\frac{2}{3} by 9x-21y.

$$\frac{1}{2}\left(14x-\frac{2}{3}\times 9x-\frac{2}{3}\left(-21\right)y-2\left(x+y\right)\right)$$

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

$$\frac{1}{2}\left(14x+\frac{-2\times 9}{3}x-\frac{2}{3}\left(-21\right)y-2\left(x+y\right)\right)$$

Multiply -2 and 9 to get -18.

$$\frac{1}{2}\left(14x+\frac{-18}{3}x-\frac{2}{3}\left(-21\right)y-2\left(x+y\right)\right)$$

Divide -18 by 3 to get -6.

$$\frac{1}{2}\left(14x-6x-\frac{2}{3}\left(-21\right)y-2\left(x+y\right)\right)$$

Express -\frac{2}{3}\left(-21\right) as a single fraction.

$$\frac{1}{2}\left(14x-6x+\frac{-2\left(-21\right)}{3}y-2\left(x+y\right)\right)$$

Multiply -2 and -21 to get 42.

$$\frac{1}{2}\left(14x-6x+\frac{42}{3}y-2\left(x+y\right)\right)$$

Divide 42 by 3 to get 14.

$$\frac{1}{2}\left(14x-6x+14y-2\left(x+y\right)\right)$$

Combine 14x and -6x to get 8x.

$$\frac{1}{2}\left(8x+14y-2\left(x+y\right)\right)$$

Use the distributive property to multiply -2 by x+y.

$$\frac{1}{2}\left(8x+14y-2x-2y\right)$$

Combine 8x and -2x to get 6x.

$$\frac{1}{2}\left(6x+14y-2y\right)$$

Combine 14y and -2y to get 12y.

$$\frac{1}{2}\left(6x+12y\right)$$

Use the distributive property to multiply \frac{1}{2} by 6x+12y.

$$\frac{1}{2}\times 6x+\frac{1}{2}\times 12y$$

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

$$\frac{6}{2}x+\frac{1}{2}\times 12y$$

Divide 6 by 2 to get 3.

$$3x+\frac{1}{2}\times 12y$$

Multiply \frac{1}{2} and 12 to get \frac{12}{2}.

$$3x+\frac{12}{2}y$$

Divide 12 by 2 to get 6.

$$3x+6y$$

Expand

$$3x+6y$$

Solution Steps

Use the distributive property to multiply -\frac{2}{3} by 9x-21y.

$$\frac{1}{2}\left(14x-\frac{2}{3}\times 9x-\frac{2}{3}\left(-21\right)y-2\left(x+y\right)\right)$$

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

$$\frac{1}{2}\left(14x+\frac{-2\times 9}{3}x-\frac{2}{3}\left(-21\right)y-2\left(x+y\right)\right)$$

Multiply -2 and 9 to get -18.

$$\frac{1}{2}\left(14x+\frac{-18}{3}x-\frac{2}{3}\left(-21\right)y-2\left(x+y\right)\right)$$

Divide -18 by 3 to get -6.

$$\frac{1}{2}\left(14x-6x-\frac{2}{3}\left(-21\right)y-2\left(x+y\right)\right)$$

Express -\frac{2}{3}\left(-21\right) as a single fraction.

$$\frac{1}{2}\left(14x-6x+\frac{-2\left(-21\right)}{3}y-2\left(x+y\right)\right)$$

Multiply -2 and -21 to get 42.

$$\frac{1}{2}\left(14x-6x+\frac{42}{3}y-2\left(x+y\right)\right)$$

Divide 42 by 3 to get 14.

$$\frac{1}{2}\left(14x-6x+14y-2\left(x+y\right)\right)$$

Combine 14x and -6x to get 8x.

$$\frac{1}{2}\left(8x+14y-2\left(x+y\right)\right)$$

Use the distributive property to multiply -2 by x+y.

$$\frac{1}{2}\left(8x+14y-2x-2y\right)$$

Combine 8x and -2x to get 6x.

$$\frac{1}{2}\left(6x+14y-2y\right)$$

Combine 14y and -2y to get 12y.

$$\frac{1}{2}\left(6x+12y\right)$$

Use the distributive property to multiply \frac{1}{2} by 6x+12y.

$$\frac{1}{2}\times 6x+\frac{1}{2}\times 12y$$

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

$$\frac{6}{2}x+\frac{1}{2}\times 12y$$

Divide 6 by 2 to get 3.

$$3x+\frac{1}{2}\times 12y$$

Multiply \frac{1}{2} and 12 to get \frac{12}{2}.

$$3x+\frac{12}{2}y$$

Divide 12 by 2 to get 6.

$$3x+6y$$