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

$$3x+2y-(2x-(3x-(2y-3x)-2x)-y)$$

Evaluate

$$5x+y$$

Solution Steps

To find the opposite of 2y-3x, find the opposite of each term.

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

The opposite of -3x is 3x.

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

Combine 3x and 3x to get 6x.

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

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

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

To find the opposite of 4x-2y, find the opposite of each term.

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

The opposite of -2y is 2y.

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

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

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

Combine 2y and -y to get y.

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

To find the opposite of -2x+y, find the opposite of each term.

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

The opposite of -2x is 2x.

$$3x+2y+2x-y$$

Combine 3x and 2x to get 5x.

$$5x+2y-y$$

Combine 2y and -y to get y.

$$5x+y$$

Expand

$$5x+y$$

Solution Steps

To find the opposite of 2y-3x, find the opposite of each term.

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

The opposite of -3x is 3x.

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

Combine 3x and 3x to get 6x.

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

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

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

To find the opposite of 4x-2y, find the opposite of each term.

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

The opposite of -2y is 2y.

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

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

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

Combine 2y and -y to get y.

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

To find the opposite of -2x+y, find the opposite of each term.

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

The opposite of -2x is 2x.

$$3x+2y+2x-y$$

Combine 3x and 2x to get 5x.

$$5x+2y-y$$

Combine 2y and -y to get y.

$$5x+y$$