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Find all real numbers \(t\) such that \(\frac{2}{3} t - 1 < t + 7 \le -2t + 15\). Give your answer as an interval.

 Apr 19, 2019
 #1
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We need to split this into two inequalities....we have....

 

(2/3)t - 1 < t + 7     rearrange as

 

-8 <  t - (2/3)t

 

-8 < (1/3)t       multiply both sides by 3

 

-24 < t

 

And

 

t + 7  ≤  -2t + 15     rearrange as

 

3t ≤ 8     divide through by  3

 

t ≤ 8/3

 

So....the solution is

 

 

-24 < t ≤  8/3

 

 

 

cool cool cool

 Apr 19, 2019

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