Solve 1/2(4x-2y)-2/3(9x-3y)-2(x-y)

$$\frac { 1 } { 2 } ( 4 x - 2 y ) - \frac { 2 } { 3 } ( 9 x - 3 y ) - 2 ( x - y )$$

Evaluate

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

Solution Steps

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

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

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

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

Divide 4 by 2 to get 2.

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

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

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

Divide -2 by 2 to get -1.

$$2x-y-\frac{2}{3}\left(9x-3y\right)-2\left(x-y\right)$$

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

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

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

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

Multiply -2 and 9 to get -18.

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

Divide -18 by 3 to get -6.

$$2x-y-6x-\frac{2}{3}\left(-3\right)y-2\left(x-y\right)$$

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

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

Multiply -2 and -3 to get 6.

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

Divide 6 by 3 to get 2.

$$2x-y-6x+2y-2\left(x-y\right)$$

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

$$-4x-y+2y-2\left(x-y\right)$$

Combine -y and 2y to get y.

$$-4x+y-2\left(x-y\right)$$

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

$$-4x+y-2x+2y$$

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

$$-6x+y+2y$$

Combine y and 2y to get 3y.

$$-6x+3y$$

Expand

$$3y-6x$$

Solution Steps

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

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

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

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

Divide 4 by 2 to get 2.

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

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

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

Divide -2 by 2 to get -1.

$$2x-y-\frac{2}{3}\left(9x-3y\right)-2\left(x-y\right)$$

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

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

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

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

Multiply -2 and 9 to get -18.

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

Divide -18 by 3 to get -6.

$$2x-y-6x-\frac{2}{3}\left(-3\right)y-2\left(x-y\right)$$

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

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

Multiply -2 and -3 to get 6.

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

Divide 6 by 3 to get 2.

$$2x-y-6x+2y-2\left(x-y\right)$$

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

$$-4x-y+2y-2\left(x-y\right)$$

Combine -y and 2y to get y.

$$-4x+y-2\left(x-y\right)$$

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

$$-4x+y-2x+2y$$

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

$$-6x+y+2y$$

Combine y and 2y to get 3y.

$$-6x+3y$$