Solve z-2(z+v)=3z-(20-5z)

$$z - 2 ( z + v ) = 3 z - ( 20 - 5 z )$$

Solve for v

$$v=-\frac{9z}{2}+10$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by z+v.

$$z-2z-2v=3z-\left(20-5z\right)$$

Combine z and -2z to get -z.

$$-z-2v=3z-\left(20-5z\right)$$

To find the opposite of 20-5z, find the opposite of each term.

$$-z-2v=3z-20+5z$$

Combine 3z and 5z to get 8z.

$$-z-2v=8z-20$$

Add z to both sides.

$$-2v=8z-20+z$$

Combine 8z and z to get 9z.

$$-2v=9z-20$$

Divide both sides by -2.

$$\frac{-2v}{-2}=\frac{9z-20}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$v=\frac{9z-20}{-2}$$

Divide 9z-20 by -2.

$$v=-\frac{9z}{2}+10$$

Solve for z

$$z=\frac{20-2v}{9}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by z+v.

$$z-2z-2v=3z-\left(20-5z\right)$$

Combine z and -2z to get -z.

$$-z-2v=3z-\left(20-5z\right)$$

To find the opposite of 20-5z, find the opposite of each term.

$$-z-2v=3z-20+5z$$

Combine 3z and 5z to get 8z.

$$-z-2v=8z-20$$

Subtract 8z from both sides.

$$-z-2v-8z=-20$$

Combine -z and -8z to get -9z.

$$-9z-2v=-20$$

Add 2v to both sides.

$$-9z=-20+2v$$

The equation is in standard form.

$$-9z=2v-20$$

Divide both sides by -9.

$$\frac{-9z}{-9}=\frac{2v-20}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$z=\frac{2v-20}{-9}$$

Divide -20+2v by -9.

$$z=\frac{20-2v}{9}$$