The inequality 1x≥3−2x\frac{1}{x} \ge 3 - 2xx1≥3−2x holds for x∈(0,12]∪[1,∞) x \in (0, \frac{1}{2}] \cup [1, \infty) x∈(0,21]∪[1,∞), and equality occurs at x=12 x = \frac{1}{2} x=21 and x=1 x = 1 x=1. It does not hold for all x>0 x > 0 x>0 (e.g., fails at x=0.75 x = 0.75 x=0.75), so the statement is true only in these intervals.
