Solve \(\frac{1}{3} t - 5 < t - 2 \le -3t + 7.\) Give your answer as an interval.
+515 the solution is: -9/2 < t ≤ 9/4
so the interval is: \((-\frac{9}{2},\:\frac{9}{4}]\)
+118677 \(\frac{1}{3} t - 5 < t - 2 \le -3t + 7\\ \frac{1}{3} t - 5 < t - 2\qquad and \qquad t - 2 \le -3t + 7\\ \frac{-2}{3} t < 3\qquad \qquad and \qquad \qquad 4 t \le 9\\ -2 t < 9\qquad \qquad and \qquad \qquad t \le 2.25\\ t > -4.5\qquad \qquad and \qquad \qquad t \le 2.25\\ -4.5\)
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