Solve 3x-[5y-{10z-(5x-10y+3z)}]

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

Evaluate

$$7z+5y-2x$$

Solution Steps

To find the opposite of 5x-10y+3z, find the opposite of each term.

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

The opposite of -10y is 10y.

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

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

$$3x-\left(5y-\left(7z-5x+10y\right)\right)$$

To find the opposite of 7z-5x+10y, find the opposite of each term.

$$3x-\left(5y-7z-\left(-5x\right)-10y\right)$$

The opposite of -5x is 5x.

$$3x-\left(5y-7z+5x-10y\right)$$

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

$$3x-\left(-5y-7z+5x\right)$$

To find the opposite of -5y-7z+5x, find the opposite of each term.

$$3x-\left(-5y\right)-\left(-7z\right)-5x$$

The opposite of -5y is 5y.

$$3x+5y-\left(-7z\right)-5x$$

The opposite of -7z is 7z.

$$3x+5y+7z-5x$$

Combine 3x and -5x to get -2x.

$$-2x+5y+7z$$

Expand

$$7z+5y-2x$$

Solution Steps

To find the opposite of 5x-10y+3z, find the opposite of each term.

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

The opposite of -10y is 10y.

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

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

$$3x-\left(5y-\left(7z-5x+10y\right)\right)$$

To find the opposite of 7z-5x+10y, find the opposite of each term.

$$3x-\left(5y-7z-\left(-5x\right)-10y\right)$$

The opposite of -5x is 5x.

$$3x-\left(5y-7z+5x-10y\right)$$

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

$$3x-\left(-5y-7z+5x\right)$$

To find the opposite of -5y-7z+5x, find the opposite of each term.

$$3x-\left(-5y\right)-\left(-7z\right)-5x$$

The opposite of -5y is 5y.

$$3x+5y-\left(-7z\right)-5x$$

The opposite of -7z is 7z.

$$3x+5y+7z-5x$$

Combine 3x and -5x to get -2x.

$$-2x+5y+7z$$