Solve 3-{2x-[1-(x+y)]+[x-2y]}

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

Evaluate

$$4+y-4x$$

Solution Steps

To find the opposite of x+y, find the opposite of each term.

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

To find the opposite of 1-x-y, find the opposite of each term.

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

The opposite of -x is x.

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

Combine 2x and x to get 3x.

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

The opposite of -y is y.

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

Combine 3x and x to get 4x.

$$3-\left(4x-1+y-2y\right)$$

Combine y and -2y to get -y.

$$3-\left(4x-1-y\right)$$

To find the opposite of 4x-1-y, find the opposite of each term.

$$3-4x-\left(-1\right)-\left(-y\right)$$

The opposite of -1 is 1.

$$3-4x+1-\left(-y\right)$$

The opposite of -y is y.

$$3-4x+1+y$$

Add 3 and 1 to get 4.

$$4-4x+y$$

Expand

$$4+y-4x$$

Solution Steps

To find the opposite of x+y, find the opposite of each term.

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

To find the opposite of 1-x-y, find the opposite of each term.

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

The opposite of -x is x.

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

Combine 2x and x to get 3x.

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

The opposite of -y is y.

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

Combine 3x and x to get 4x.

$$3-\left(4x-1+y-2y\right)$$

Combine y and -2y to get -y.

$$3-\left(4x-1-y\right)$$

To find the opposite of 4x-1-y, find the opposite of each term.

$$3-4x-\left(-1\right)-\left(-y\right)$$

The opposite of -1 is 1.

$$3-4x+1-\left(-y\right)$$

The opposite of -y is y.

$$3-4x+1+y$$

Add 3 and 1 to get 4.

$$4-4x+y$$