Solve (z-1)-(z-3)=1/3[z+3)+1/2

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

Solve for z

$$z = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

To find the opposite of z-3, find the opposite of each term.

$$z-1-z-\left(-3\right)=\frac{1}{3}\left(z+3\right)+\frac{1}{2}$$

The opposite of -3 is 3.

$$z-1-z+3=\frac{1}{3}\left(z+3\right)+\frac{1}{2}$$

Combine z and -z to get 0.

$$-1+3=\frac{1}{3}\left(z+3\right)+\frac{1}{2}$$

Add -1 and 3 to get 2.

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

Use the distributive property to multiply \frac{1}{3} by z+3.

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

Cancel out 3 and 3.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

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

Swap sides so that all variable terms are on the left hand side.

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

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

$$\frac{1}{3}z=2-\frac{3}{2}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{1}{3}z=\frac{4}{2}-\frac{3}{2}$$

Since \frac{4}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}z=\frac{4-3}{2}$$

Subtract 3 from 4 to get 1.

$$\frac{1}{3}z=\frac{1}{2}$$

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

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

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$z=\frac{3}{2}$$