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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

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