Solve 3(7-z)-41=21z-4(5+6z)

$$3 ( 7 - z ) - 41 = 21 z - 4 ( 5 + 6 z )$$

Solve for z

$$z\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 3 by 7-z.

$$21-3z-41=21z-4\left(5+6z\right)$$

Subtract 41 from 21 to get -20.

$$-20-3z=21z-4\left(5+6z\right)$$

Use the distributive property to multiply -4 by 5+6z.

$$-20-3z=21z-20-24z$$

Combine 21z and -24z to get -3z.

$$-20-3z=-3z-20$$

Add 3z to both sides.

$$-20-3z+3z=-20$$

Combine -3z and 3z to get 0.

$$-20=-20$$

Compare -20 and -20.

$$\text{true}$$

This is true for any z.

$$z\in \mathrm{R}$$