First you rewrite 1 2/3 into an improper fraction: z-1/3=5/3
Then you have: z-1/3=5/3
Move -1/3 to the right side of the equation by adding 1/3 to both sides.
z=1/3+5/3
Simplify the right side by combining the numerators over the common denominator: z=(1+5)/3
Add 1 and 5 to get 6: z=6/3
Divide 6 by 3 and get 2
z=2