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4 years ago

15

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

1 answer:

Andrews [41]4 years ago

8 0

Break up chain with AND statement:

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

left side, we solve for t
</span>
<span>(2/3)t - 1 < t + 7
(2/3)t - t < 7 + 1
(-1/3)t < 8
t > -24

right side, we solve for t</span>
<span>t + 7 ≤ -2t + 15
t + 2t </span><span>≤ 15 - 7
3t </span><span>≤ 8
t </span><span>≤ 8/3

So our answer would be </span>
t > -24 AND t <span>≤ 8/3

as an interval, this is
</span>-24 < t <span>≤ 8/3
or in interval notation
(-24, 8/3]</span>

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