If x ∈ I, then the solution set of the inequation 1 < 3x + 5 ≤ 11 is

1. { -1, 0, 1, 2}
2. { -2, -1, 0, 1}
3. { -1, 0, 1}
4. {x : x ∈ R, -$\dfrac{4}{3}$ $\lt$ x $\le$ 2}

x ∈ I

Given,
1 < 3x + 5 ≤ 11

Solving left side,

$\Rightarrow 1 \lt 3x + 5 \\[0.5em] \Rightarrow 1 - 5 \lt 3x \\[0.5em] \Rightarrow -4 \lt 3x \\[0.5em] \Rightarrow 3x \gt -4 \\[0.5em] \Rightarrow x \gt -\dfrac{4}{3}$

Solving right side,

$3x + 5 \le 11 \\[0.5em] \Rightarrow 3x \le 11-5 \\[0.5em] \Rightarrow 3x \le 6 \\[0.5em] \Rightarrow x \le 2 \\[1.5em] \therefore -\dfrac{4}{3} \lt x \le 2$

Solution set = {-1, 0, 1, 2}.

∴ Option 1 is the correct option.