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