\(\frac{t}{3} - 5 < t - 2 + 2t \le -3t + 7\)
\(t - 15 < 3t - 6 + 6t \le -9t + 21\)
\(t - 15 < 9t - 6 \le -9t + 21\)
\(-15 < 8t - 6 \le -10t + 21\)
\(8t - 6 \le -10t + 21\)
\(18t \le 27\)
\(t \le \frac{3}{2}\)
\(-15 < 8t - 6\)
\(-9 < 8t\)
\(t > -\frac{9}{8}\)
\(\boxed{t = (-\frac{9}{8}, \frac{3}{2}]}\)
.