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# halp!

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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