Solve 1/2x-2(x-1/2y)-6(1/3x+1/2y)+frac{7}{2}x

$$\frac { 1 } { 2 } x - 2 ( x - \frac { 1 } { 2 } y ) - 6 ( \frac { 1 } { 3 } x + \frac { 1 } { 2 } y ) + \frac { 7 } { 2 } x$$

Evaluate

$$-2y$$

Solution Steps

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

$$\frac{1}{2}x-2x-2\left(-\frac{1}{2}\right)y-6\left(\frac{1}{3}x+\frac{1}{2}y\right)+\frac{7}{2}x$$

Multiply -2 times -\frac{1}{2}.

$$\frac{1}{2}x-2x+y-6\left(\frac{1}{3}x+\frac{1}{2}y\right)+\frac{7}{2}x$$

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

$$-\frac{3}{2}x+y-6\left(\frac{1}{3}x+\frac{1}{2}y\right)+\frac{7}{2}x$$

Use the distributive property to multiply -6 by \frac{1}{3}x+\frac{1}{2}y.

$$-\frac{3}{2}x+y-6\times \frac{1}{3}x-6\times \frac{1}{2}y+\frac{7}{2}x$$

Multiply -6 and \frac{1}{3} to get \frac{-6}{3}.

$$-\frac{3}{2}x+y+\frac{-6}{3}x-6\times \frac{1}{2}y+\frac{7}{2}x$$

Divide -6 by 3 to get -2.

$$-\frac{3}{2}x+y-2x-6\times \frac{1}{2}y+\frac{7}{2}x$$

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

$$-\frac{3}{2}x+y-2x+\frac{-6}{2}y+\frac{7}{2}x$$

Divide -6 by 2 to get -3.

$$-\frac{3}{2}x+y-2x-3y+\frac{7}{2}x$$

Combine -\frac{3}{2}x and -2x to get -\frac{7}{2}x.

$$-\frac{7}{2}x+y-3y+\frac{7}{2}x$$

Combine y and -3y to get -2y.

$$-\frac{7}{2}x-2y+\frac{7}{2}x$$

Combine -\frac{7}{2}x and \frac{7}{2}x to get 0.

$$-2y$$

Expand

$$-2y$$

Solution Steps

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

$$\frac{1}{2}x-2x-2\left(-\frac{1}{2}\right)y-6\left(\frac{1}{3}x+\frac{1}{2}y\right)+\frac{7}{2}x$$

Multiply -2 times -\frac{1}{2}.

$$\frac{1}{2}x-2x+y-6\left(\frac{1}{3}x+\frac{1}{2}y\right)+\frac{7}{2}x$$

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

$$-\frac{3}{2}x+y-6\left(\frac{1}{3}x+\frac{1}{2}y\right)+\frac{7}{2}x$$

Use the distributive property to multiply -6 by \frac{1}{3}x+\frac{1}{2}y.

$$-\frac{3}{2}x+y-6\times \frac{1}{3}x-6\times \frac{1}{2}y+\frac{7}{2}x$$

Multiply -6 and \frac{1}{3} to get \frac{-6}{3}.

$$-\frac{3}{2}x+y+\frac{-6}{3}x-6\times \frac{1}{2}y+\frac{7}{2}x$$

Divide -6 by 3 to get -2.

$$-\frac{3}{2}x+y-2x-6\times \frac{1}{2}y+\frac{7}{2}x$$

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

$$-\frac{3}{2}x+y-2x+\frac{-6}{2}y+\frac{7}{2}x$$

Divide -6 by 2 to get -3.

$$-\frac{3}{2}x+y-2x-3y+\frac{7}{2}x$$

Combine -\frac{3}{2}x and -2x to get -\frac{7}{2}x.

$$-\frac{7}{2}x+y-3y+\frac{7}{2}x$$

Combine y and -3y to get -2y.

$$-\frac{7}{2}x-2y+\frac{7}{2}x$$

Combine -\frac{7}{2}x and \frac{7}{2}x to get 0.

$$-2y$$