Solve 6(t+2)-7z=2(-1/2z+1)+10

$$6 ( t + 2 ) - 7 z = 2 ( - \frac { 1 } { 2 } z + 1 ) + 10$$

Solve for t

$$t=z$$

Solution Steps

Use the distributive property to multiply 6 by t+2.

$$6t+12-7z=2\left(-\frac{1}{2}z+1\right)+10$$

Use the distributive property to multiply 2 by -\frac{1}{2}z+1.

$$6t+12-7z=-z+2+10$$

Add 2 and 10 to get 12.

$$6t+12-7z=-z+12$$

Subtract 12 from both sides.

$$6t-7z=-z+12-12$$

Subtract 12 from 12 to get 0.

$$6t-7z=-z$$

Add 7z to both sides.

$$6t=-z+7z$$

Combine -z and 7z to get 6z.

$$6t=6z$$

Cancel out 6 on both sides.

$$t=z$$

Solve for z

$$z=t$$

Solution Steps

Use the distributive property to multiply 6 by t+2.

$$6t+12-7z=2\left(-\frac{1}{2}z+1\right)+10$$

Use the distributive property to multiply 2 by -\frac{1}{2}z+1.

$$6t+12-7z=-z+2+10$$

Add 2 and 10 to get 12.

$$6t+12-7z=-z+12$$

Add z to both sides.

$$6t+12-7z+z=12$$

Combine -7z and z to get -6z.

$$6t+12-6z=12$$

Subtract 6t from both sides.

$$12-6z=12-6t$$

Subtract 12 from both sides.

$$-6z=12-6t-12$$

Subtract 12 from 12 to get 0.

$$-6z=-6t$$

Cancel out -6 on both sides.

$$z=t$$