Solve $\frac{1}{3} t - 5 < t - 2 \le -3t + 7.$ Give your answer as an interval.
I'm getting 4//5 < t <= 5/2, so in interval notation the solution is \((4/5,5/2]\)
We have two equations here
t/3 - 5 < t - 2 t - 2 ≤ -3t + 7
-5 + 2 < t -t/3 t + 3t ≤ 7 + 2
-3 < (2/3)t 4t ≤ 9
-3(3/2) < t t ≤ 9/4
-9/2 < t
-9/2 < t ≤ 9/4