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Find all real numbers T such that (2/3)t - 1 < t + 7 ≤ -2t + 15. 

 

 

Thanks,

 Oct 15, 2019
 #1
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(2/3)t - 1 < t + 7 ≤ -2t + 15

 

We can split this up into two inequalities

 

(2/3)t - 1  < t +7                                               t + 7  ≤-2t + 15

 

add 1 to both sides,                                         add 2t to both sides,

subtract t from both sides                                subtract 7 from both sides

 

(-1/3)t <  8                                                         3t ≤ 8

 

Multiply both sides by - 3                                     divide both sides by  3

Change the direction of the inequality sign

 

t >  - 24                                                                   t ≤ 8/3

 

So  ....the answer is that

 

-24 < t ≤ 8/3

 

 

cool cool cool

 Oct 15, 2019

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