Solve 2x+3y-11-(3xy-2x+1/2)+(xy-3x-2y+1/2-y)

$$2 x + 3 y - 11 - ( 3 x y - 2 x + \frac { 1 } { 2 } ) + ( x y - 3 x - 2 y + \frac { 1 } { 2 } - y )$$

Evaluate

$$-2xy+x-11$$

Solution Steps

To find the opposite of 3xy-2x+\frac{1}{2}, find the opposite of each term.

$$2x+3y-11-3xy-\left(-2x\right)-\frac{1}{2}+xy-3x-2y+\frac{1}{2}-y$$

The opposite of -2x is 2x.

$$2x+3y-11-3xy+2x-\frac{1}{2}+xy-3x-2y+\frac{1}{2}-y$$

Combine 2x and 2x to get 4x.

$$4x+3y-11-3xy-\frac{1}{2}+xy-3x-2y+\frac{1}{2}-y$$

Convert -11 to fraction -\frac{22}{2}.

$$4x+3y-\frac{22}{2}-3xy-\frac{1}{2}+xy-3x-2y+\frac{1}{2}-y$$

Since -\frac{22}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$4x+3y+\frac{-22-1}{2}-3xy+xy-3x-2y+\frac{1}{2}-y$$

Subtract 1 from -22 to get -23.

$$4x+3y-\frac{23}{2}-3xy+xy-3x-2y+\frac{1}{2}-y$$

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

$$4x+3y-\frac{23}{2}-2xy-3x-2y+\frac{1}{2}-y$$

Combine 4x and -3x to get x.

$$x+3y-\frac{23}{2}-2xy-2y+\frac{1}{2}-y$$

Combine 3y and -2y to get y.

$$x+y-\frac{23}{2}-2xy+\frac{1}{2}-y$$

Since -\frac{23}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$x+y+\frac{-23+1}{2}-2xy-y$$

Add -23 and 1 to get -22.

$$x+y+\frac{-22}{2}-2xy-y$$

Divide -22 by 2 to get -11.

$$x+y-11-2xy-y$$

Combine y and -y to get 0.

$$x-11-2xy$$

Expand

$$-2xy+x-11$$

Solution Steps

To find the opposite of 3xy-2x+\frac{1}{2}, find the opposite of each term.

$$2x+3y-11-3xy-\left(-2x\right)-\frac{1}{2}+xy-3x-2y+\frac{1}{2}-y$$

The opposite of -2x is 2x.

$$2x+3y-11-3xy+2x-\frac{1}{2}+xy-3x-2y+\frac{1}{2}-y$$

Combine 2x and 2x to get 4x.

$$4x+3y-11-3xy-\frac{1}{2}+xy-3x-2y+\frac{1}{2}-y$$

Convert -11 to fraction -\frac{22}{2}.

$$4x+3y-\frac{22}{2}-3xy-\frac{1}{2}+xy-3x-2y+\frac{1}{2}-y$$

Since -\frac{22}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$4x+3y+\frac{-22-1}{2}-3xy+xy-3x-2y+\frac{1}{2}-y$$

Subtract 1 from -22 to get -23.

$$4x+3y-\frac{23}{2}-3xy+xy-3x-2y+\frac{1}{2}-y$$

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

$$4x+3y-\frac{23}{2}-2xy-3x-2y+\frac{1}{2}-y$$

Combine 4x and -3x to get x.

$$x+3y-\frac{23}{2}-2xy-2y+\frac{1}{2}-y$$

Combine 3y and -2y to get y.

$$x+y-\frac{23}{2}-2xy+\frac{1}{2}-y$$

Since -\frac{23}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$x+y+\frac{-23+1}{2}-2xy-y$$

Add -23 and 1 to get -22.

$$x+y+\frac{-22}{2}-2xy-y$$

Divide -22 by 2 to get -11.

$$x+y-11-2xy-y$$

Combine y and -y to get 0.

$$x-11-2xy$$