Solve -2+2[3-(-2x+y)+2(x-3y)]-4(2x-y+1)

$$- 2 + 2 [ 3 - ( - 2 x + y ) + 2 ( x - 3 y ) ] - 4 ( 2 x - y + 1 )$$

Evaluate

$$-10y$$

Solution Steps

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

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

The opposite of -2x is 2x.

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

Use the distributive property to multiply 2 by x-3y.

$$-2+2\left(3+2x-y+2x-6y\right)-4\left(2x-y+1\right)$$

Combine 2x and 2x to get 4x.

$$-2+2\left(3+4x-y-6y\right)-4\left(2x-y+1\right)$$

Combine -y and -6y to get -7y.

$$-2+2\left(3+4x-7y\right)-4\left(2x-y+1\right)$$

Use the distributive property to multiply 2 by 3+4x-7y.

$$-2+6+8x-14y-4\left(2x-y+1\right)$$

Add -2 and 6 to get 4.

$$4+8x-14y-4\left(2x-y+1\right)$$

Use the distributive property to multiply -4 by 2x-y+1.

$$4+8x-14y-8x+4y-4$$

Combine 8x and -8x to get 0.

$$4-14y+4y-4$$

Combine -14y and 4y to get -10y.

$$4-10y-4$$

Subtract 4 from 4 to get 0.

$$-10y$$

Expand

$$-10y$$

Solution Steps

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

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

The opposite of -2x is 2x.

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

Use the distributive property to multiply 2 by x-3y.

$$-2+2\left(3+2x-y+2x-6y\right)-4\left(2x-y+1\right)$$

Combine 2x and 2x to get 4x.

$$-2+2\left(3+4x-y-6y\right)-4\left(2x-y+1\right)$$

Combine -y and -6y to get -7y.

$$-2+2\left(3+4x-7y\right)-4\left(2x-y+1\right)$$

Use the distributive property to multiply 2 by 3+4x-7y.

$$-2+6+8x-14y-4\left(2x-y+1\right)$$

Add -2 and 6 to get 4.

$$4+8x-14y-4\left(2x-y+1\right)$$

Use the distributive property to multiply -4 by 2x-y+1.

$$4+8x-14y-8x+4y-4$$

Combine 8x and -8x to get 0.

$$4-14y+4y-4$$

Combine -14y and 4y to get -10y.

$$4-10y-4$$

Subtract 4 from 4 to get 0.

$$-10y$$