If x ∈ R, the solution set of 6 ≤ -3(2x - 4) < 12 is

1. {x : x ∈ R, 0 < x ≤ 1}
2. {x : x ∈ R, 0 ≤ x < 1}
3. {0, 1}
4. none of these

x ∈ R

Given,
6 ≤ -3(2x - 4) < 12

Solving left side,

$6 \le -3(2x - 4) \\[0.5em] \Rightarrow 6 \le - 6x + 12 \\[0.5em] \Rightarrow 6-12 \le -6x \\[0.5em] \Rightarrow -6 \le -6x \\[0.5em] \Rightarrow 6x \le 6 \\[0.5em] \Rightarrow x \le 1$

Solving right side,

$-3(2x - 4) \lt 12 \\[0.5em] \Rightarrow -6x + 12 \lt 12 \\[0.5em] \Rightarrow -6x \lt 12-12 \\[0.5em] \Rightarrow -6x \lt 0 \\[0.5em] \Rightarrow x \gt 0 \\[1.5em] \therefore 0 \lt x \le 1$

Solution set = {x : x ∈ R, 0 $\lt x \le$ 1}

∴ Option 1 is the correct option.