Solve 10y-10x-{-2x+9y-3z-[-8x+2y-5z+(6x-5z)]}

$$10 y - 10 x - \{ - 2 x + 9 y - 3 z - [ - 8 x + 2 y - 5 z + ( 6 x - 5 z ) ] \}$$

Evaluate

$$-10x+3y-7z$$

Solution Steps

Combine -8x and 6x to get -2x.

$$10y-10x-\left(-2x+9y-3z-\left(-2x+2y-5z-5z\right)\right)$$

Combine -5z and -5z to get -10z.

$$10y-10x-\left(-2x+9y-3z-\left(-2x+2y-10z\right)\right)$$

To find the opposite of -2x+2y-10z, find the opposite of each term.

$$10y-10x-\left(-2x+9y-3z-\left(-2x\right)-2y-\left(-10z\right)\right)$$

The opposite of -2x is 2x.

$$10y-10x-\left(-2x+9y-3z+2x-2y-\left(-10z\right)\right)$$

The opposite of -10z is 10z.

$$10y-10x-\left(-2x+9y-3z+2x-2y+10z\right)$$

Combine -2x and 2x to get 0.

$$10y-10x-\left(9y-3z-2y+10z\right)$$

Combine 9y and -2y to get 7y.

$$10y-10x-\left(7y-3z+10z\right)$$

Combine -3z and 10z to get 7z.

$$10y-10x-\left(7y+7z\right)$$

To find the opposite of 7y+7z, find the opposite of each term.

$$10y-10x-7y-7z$$

Combine 10y and -7y to get 3y.

$$3y-10x-7z$$

Expand

$$-10x+3y-7z$$

Solution Steps

Combine -8x and 6x to get -2x.

$$10y-10x-\left(-2x+9y-3z-\left(-2x+2y-5z-5z\right)\right)$$

Combine -5z and -5z to get -10z.

$$10y-10x-\left(-2x+9y-3z-\left(-2x+2y-10z\right)\right)$$

To find the opposite of -2x+2y-10z, find the opposite of each term.

$$10y-10x-\left(-2x+9y-3z-\left(-2x\right)-2y-\left(-10z\right)\right)$$

The opposite of -2x is 2x.

$$10y-10x-\left(-2x+9y-3z+2x-2y-\left(-10z\right)\right)$$

The opposite of -10z is 10z.

$$10y-10x-\left(-2x+9y-3z+2x-2y+10z\right)$$

Combine -2x and 2x to get 0.

$$10y-10x-\left(9y-3z-2y+10z\right)$$

Combine 9y and -2y to get 7y.

$$10y-10x-\left(7y-3z+10z\right)$$

Combine -3z and 10z to get 7z.

$$10y-10x-\left(7y+7z\right)$$

To find the opposite of 7y+7z, find the opposite of each term.

$$10y-10x-7y-7z$$

Combine 10y and -7y to get 3y.

$$3y-10x-7z$$