Find all real numbers t such that (2/3) t - 1 < t + 7 ≤ - 2t + 15. Give your answer as an interval.

Break up chain with AND statement:

(2/3) t - 1 < t + 7 AND t + 7 ≤ - 2t + 15

left side, we solve for t

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

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

(-1/3) t < 8

t > - 24

right side, we solve for t

t + 7 ≤ - 2t + 15

t + 2t ≤ 15 - 7

3t ≤ 8

t ≤ 8/3

So our answer would be

t > - 24 AND t ≤ 8/3

as an interval, this is

-24 < t ≤ 8/3

or in interval notation

(-24, 8/3]