Inequality

$\frac{t}{3} - 5 < t - 2 + 2t \le -3t + 7$

$t - 15 < 3t - 6 + 6t \le -9t + 21$

$t - 15 < 9t - 6 \le -9t + 21$

$-15 < 8t - 6 \le -10t + 21$

$8t - 6 \le -10t + 21$

$18t \le 27$

$t \le \frac{3}{2}$

$-15 < 8t - 6$

$-9 < 8t$

$t > -\frac{9}{8}$

$\boxed{t = (-\frac{9}{8}, \frac{3}{2}]}$