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Find all real numbers t$ such that 2/3 t - 1 < t + 7 \le -2t + 15$. Give your answer as an interval.

 Jun 1, 2019
 #1
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Find all real numbers \(t\) such that \(\frac23 t - 1 \ <\ t + 7\ \le\ -2t + 15\) . Give your answer as an interval.

_________

 

\(\frac23 t - 1 \ <\ t + 7\\~\\ \frac23 t - t \ <\ 1 + 7\\~\\ -\frac13t\ <\ 8\\~\\ t\ >\ -24\)

 

And

 

\(t + 7\ \le\ -2t + 15\\~\\ t+2t\ \leq\ -7+15\\~\\ 3t\ \leq\ 8\\~\\ t\leq\frac83\)

 

t  is bigger than  -24  but less than or equal to  8/3

t  must be in the interval  \(\Big(-24,\frac83\Big]\)_

 Jun 2, 2019

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