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# Inequality

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Solve t/3 - 5 < t - 2 + 2t <= -3t + 7.

Apr 24, 2022

#1
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$$\frac{t}{3} - 5 < t - 2 + 2t \le -3t + 7$$

$$t - 15 < 3t - 6 + 6t \le -9t + 21$$

$$t - 15 < 9t - 6 \le -9t + 21$$

$$-15 < 8t - 6 \le -10t + 21$$

$$8t - 6 \le -10t + 21$$

$$18t \le 27$$

$$t \le \frac{3}{2}$$

$$-15 < 8t - 6$$

$$-9 < 8t$$

$$t > -\frac{9}{8}$$

$$\boxed{t = (-\frac{9}{8}, \frac{3}{2}]}$$

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Apr 24, 2022