+23252 First -- simplify the middle expression: t - 2 + 7 = t + 5.
We now have: t/3 - 5 < t + 5 <= - 3t
Divide this into two inequalities: t/3 - 5 < t + 5 and t + 5 <= -3t
Solve each one independently: t - 15 < 3t + 15 4t <= -5
-30 < 2t t <= -5/4
-15 < t
Combining these answers: -15 < t <= -5/4
