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Solve \(\frac{1}{3} t - 5 < t - 2 \le -3t + 7\) Give your answer as an interval.

 Jul 8, 2020
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We break the inequality down into two inequalities: \(\frac{1}{3}t-5 . We solve for  \(\frac{1}{3}t-5  first.

 

\(\frac{1}{3}t-5 -\frac{9}{2}\)

 

Then we solve for \(t-2\le-3t+7\).

 

\(t-2\le-3t+7\\ = 4t\le9\\ = t\le\frac{9}{4}\)

 

Then t must be \(-\frac{9}{2} . In interval notation this is  \(\boxed{(-\frac{9}{2}, \frac{9}{4}]}\).

 Jul 8, 2020

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