Find all real numbers \(t\) such that \(\frac{2}{3} t - 1 < t + 7 \le -2t + 15\). Give your answer as an interval.

We need to split this into two inequalities....we have....

(2/3)t - 1 < t + 7 rearrange as

-8 < t - (2/3)t

-8 < (1/3)t multiply both sides by 3

-24 < t

And

t + 7 ≤ -2t + 15 rearrange as

3t ≤ 8 divide through by 3

t ≤ 8/3

So....the solution is

-24 < t ≤ 8/3