Solve (18x-(15y+16z-12x)-(13x+20y)-(x+y+z)

$$( 18 x - ( 15 y + 16 z - 12 x ) - ( 13 x + 20 y ) - ( x + y + z )$$

Evaluate

$$16x-36y-17z$$

Solution Steps

To find the opposite of 15y+16z-12x, find the opposite of each term.

$$18x-15y-16z-\left(-12x\right)-\left(13x+20y\right)-\left(x+y+z\right)$$

The opposite of -12x is 12x.

$$18x-15y-16z+12x-\left(13x+20y\right)-\left(x+y+z\right)$$

Combine 18x and 12x to get 30x.

$$30x-15y-16z-\left(13x+20y\right)-\left(x+y+z\right)$$

To find the opposite of 13x+20y, find the opposite of each term.

$$30x-15y-16z-13x-20y-\left(x+y+z\right)$$

Combine 30x and -13x to get 17x.

$$17x-15y-16z-20y-\left(x+y+z\right)$$

Combine -15y and -20y to get -35y.

$$17x-35y-16z-\left(x+y+z\right)$$

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

$$17x-35y-16z-x-y-z$$

Combine 17x and -x to get 16x.

$$16x-35y-16z-y-z$$

Combine -35y and -y to get -36y.

$$16x-36y-16z-z$$

Combine -16z and -z to get -17z.

$$16x-36y-17z$$

Expand

$$16x-36y-17z$$

Solution Steps

To find the opposite of 15y+16z-12x, find the opposite of each term.

$$18x-15y-16z-\left(-12x\right)-\left(13x+20y\right)-\left(x+y+z\right)$$

The opposite of -12x is 12x.

$$18x-15y-16z+12x-\left(13x+20y\right)-\left(x+y+z\right)$$

Combine 18x and 12x to get 30x.

$$30x-15y-16z-\left(13x+20y\right)-\left(x+y+z\right)$$

To find the opposite of 13x+20y, find the opposite of each term.

$$30x-15y-16z-13x-20y-\left(x+y+z\right)$$

Combine 30x and -13x to get 17x.

$$17x-15y-16z-20y-\left(x+y+z\right)$$

Combine -15y and -20y to get -35y.

$$17x-35y-16z-\left(x+y+z\right)$$

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

$$17x-35y-16z-x-y-z$$

Combine 17x and -x to get 16x.

$$16x-35y-16z-y-z$$

Combine -35y and -y to get -36y.

$$16x-36y-16z-z$$

Combine -16z and -z to get -17z.

$$16x-36y-17z$$