+334 Solve \(\frac{1}{3} t - 5 < t - 2 \le -3t + 7\) Give your answer as an interval.
+781 We break the inequality down into two inequalities: \(\frac{1}{3}t-5 . We solve for \(\frac{1}{3}t-5 first.
\(\frac{1}{3}t-5 -\frac{9}{2}\)
Then we solve for \(t-2\le-3t+7\).
\(t-2\le-3t+7\\ = 4t\le9\\ = t\le\frac{9}{4}\)
Then t must be \(-\frac{9}{2} . In interval notation this is \(\boxed{(-\frac{9}{2}, \frac{9}{4}]}\).
