Solve 1/2(x-2y)+1/3(3y-2x)

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

Evaluate

$$-\frac{x}{6}$$

Solution Steps

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

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

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

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

Divide -2 by 2 to get -1.

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

Use the distributive property to multiply \frac{1}{3} by 3y-2x.

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

Cancel out 3 and 3.

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

Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.

$$\frac{1}{2}x-y+y+\frac{-2}{3}x$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{1}{2}x-y+y-\frac{2}{3}x$$

Combine -y and y to get 0.

$$\frac{1}{2}x-\frac{2}{3}x$$

Combine \frac{1}{2}x and -\frac{2}{3}x to get -\frac{1}{6}x.

$$-\frac{1}{6}x$$

Expand

$$-\frac{x}{6}$$

Solution Steps

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

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

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

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

Divide -2 by 2 to get -1.

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

Use the distributive property to multiply \frac{1}{3} by 3y-2x.

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

Cancel out 3 and 3.

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

Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.

$$\frac{1}{2}x-y+y+\frac{-2}{3}x$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{1}{2}x-y+y-\frac{2}{3}x$$

Combine -y and y to get 0.

$$\frac{1}{2}x-\frac{2}{3}x$$

Combine \frac{1}{2}x and -\frac{2}{3}x to get -\frac{1}{6}x.

$$-\frac{1}{6}x$$