Solve 3(3x+z)-(x-z)=6(x+z)

$$3(3x+z)-(x-z)=6(x+z)$$

Solve for x

$$x=z$$

Solution Steps

Use the distributive property to multiply 3 by 3x+z.

$$9x+3z-\left(x-z\right)=6\left(x+z\right)$$

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

$$9x+3z-x+z=6\left(x+z\right)$$

Combine 9x and -x to get 8x.

$$8x+3z+z=6\left(x+z\right)$$

Combine 3z and z to get 4z.

$$8x+4z=6\left(x+z\right)$$

Use the distributive property to multiply 6 by x+z.

$$8x+4z=6x+6z$$

Subtract 6x from both sides.

$$8x+4z-6x=6z$$

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

$$2x+4z=6z$$

Subtract 4z from both sides.

$$2x=6z-4z$$

Combine 6z and -4z to get 2z.

$$2x=2z$$

Cancel out 2 on both sides.

$$x=z$$

Solve for z

$$z=x$$

Solution Steps

Use the distributive property to multiply 3 by 3x+z.

$$9x+3z-\left(x-z\right)=6\left(x+z\right)$$

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

$$9x+3z-x+z=6\left(x+z\right)$$

Combine 9x and -x to get 8x.

$$8x+3z+z=6\left(x+z\right)$$

Combine 3z and z to get 4z.

$$8x+4z=6\left(x+z\right)$$

Use the distributive property to multiply 6 by x+z.

$$8x+4z=6x+6z$$

Subtract 6z from both sides.

$$8x+4z-6z=6x$$

Combine 4z and -6z to get -2z.

$$8x-2z=6x$$

Subtract 8x from both sides.

$$-2z=6x-8x$$

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

$$-2z=-2x$$

Cancel out -2 on both sides.

$$z=x$$