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

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

Evaluate

$$2x$$

Solution Steps

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

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

The opposite of -3x is 3x.

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

Combine 3x and 3x to get 6x.

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

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

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

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

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

The opposite of -2y is 2y.

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

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

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

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

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

The opposite of -2x is 2x.

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

Combine 2y and -2y to get 0.

$$2x$$

Expand

$$2x$$

Solution Steps

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

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

The opposite of -3x is 3x.

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

Combine 3x and 3x to get 6x.

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

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

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

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

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

The opposite of -2y is 2y.

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

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

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

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

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

The opposite of -2x is 2x.

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

Combine 2y and -2y to get 0.

$$2x$$