The solution set for 0 < $-\frac{x}{3}$ < 2, x ∈ Z is;

Given, 0 < $-\frac{x}{3}$ < 2

Solving L.H.S. of equation :

⇒ 0 < $-\frac{x}{3}$

⇒ $\frac{x}{3}$ < 0

⇒ x < 0 × 3

⇒ x < 0................... (1)

Solving R.H.S. of equation :

⇒ $-\frac{x}{3}$ < 2

⇒ -x < 2 × 3

⇒ -x < 6

⇒ x > -6 .................... (2)

From, equation (1) and (2), we get

-6 < x < 0 and x ∈ Z.

Solution set for x = {-5, -4, -3, -2, -1}.

Hence, option 1 is the correct option.