Answer
$\frac{5}{6}, 1, \sqrt5, 3, 5$
Work Step by Step
Add 2 to both sides of the inequality:
$-2+3x+2 \ge \frac{1}{3}+2
\\3x \ge \frac{1}{3} + \frac{6}{3}
\\3x \ge \frac{7}{3}$
Divide both sides of the inequality by $3$:
$\dfrac{3x}{3} \ge \dfrac{\frac{7}{3}}{3}
\\x \ge \frac{7}{9}$
Thus, the elements of $S$ that satisfy the inequality are:
$\frac{5}{6}, 1, \sqrt5, 3, 5$
