Solve -(y+z)+-(y+x)+-(x+z)=0

$$-(y+z)+-(y+x)+-(x+z)=0$$

Solve for x

$$x=-y-z$$

Steps for Solving Linear Equation

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

$$-y-z-\left(y+x\right)-\left(x+z\right)=0$$

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

$$-y-z-y-x-\left(x+z\right)=0$$

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

$$-2y-z-x-\left(x+z\right)=0$$

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

$$-2y-z-x-x-z=0$$

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

$$-2y-z-2x-z=0$$

Combine -z and -z to get -2z.

$$-2y-2z-2x=0$$

Add 2y to both sides. Anything plus zero gives itself.

$$-2z-2x=2y$$

Add 2z to both sides.

$$-2x=2y+2z$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{2y+2z}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{2y+2z}{-2}$$

Divide 2y+2z by -2.

$$x=-\left(y+z\right)$$

Solve for y

$$y=-x-z$$

Steps for Solving Linear Equation

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

$$-y-z-\left(y+x\right)-\left(x+z\right)=0$$

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

$$-y-z-y-x-\left(x+z\right)=0$$

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

$$-2y-z-x-\left(x+z\right)=0$$

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

$$-2y-z-x-x-z=0$$

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

$$-2y-z-2x-z=0$$

Combine -z and -z to get -2z.

$$-2y-2z-2x=0$$

Add 2z to both sides. Anything plus zero gives itself.

$$-2y-2x=2z$$

Add 2x to both sides.

$$-2y=2z+2x$$

The equation is in standard form.

$$-2y=2x+2z$$

Divide both sides by -2.

$$\frac{-2y}{-2}=\frac{2x+2z}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$y=\frac{2x+2z}{-2}$$

Divide 2z+2x by -2.

$$y=-\left(x+z\right)$$