Question

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

Answer 1

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]