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30 July, 04:41

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

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  1. 30 July, 07:40
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    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]
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