Solve 1/2z+6=3/2(z+6)

$$\frac { 1 } { 2 } z + 6 = \frac { 3 } { 2 } ( z + 6 )$$

Solve for z

$$z=-3$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{2} by z+6.

$$\frac{1}{2}z+6=\frac{3}{2}z+\frac{3}{2}\times 6$$

Express \frac{3}{2}\times 6 as a single fraction.

$$\frac{1}{2}z+6=\frac{3}{2}z+\frac{3\times 6}{2}$$

Multiply 3 and 6 to get 18.

$$\frac{1}{2}z+6=\frac{3}{2}z+\frac{18}{2}$$

Divide 18 by 2 to get 9.

$$\frac{1}{2}z+6=\frac{3}{2}z+9$$

Subtract \frac{3}{2}z from both sides.

$$\frac{1}{2}z+6-\frac{3}{2}z=9$$

Combine \frac{1}{2}z and -\frac{3}{2}z to get -z.

$$-z+6=9$$

Subtract 6 from both sides.

$$-z=9-6$$

Subtract 6 from 9 to get 3.

$$-z=3$$

Multiply both sides by -1.

$$z=-3$$