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For how many positive integral values of a is it true that x = 2 is the only positive integer solution of the system of inequalities \(\begin{cases} 2x>3x-3\\ 3x-a>-6 \end{cases}\)

 Apr 26, 2019
 #1
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2x > 3x - 3  ⇒  2x + 3 > 3x

3x - a > -6 ⇒   3x > a - 6

 

So....we have the combined inequality.....

 

a - 6 < 3x < 2x + 3          and when x  = 2

 

a - 6 < 3(2) < 2(2) + 3          

 

a - 6 < 6 < 7          add 6 to each term

 

a < 12 < 13

 

So  a  =  [ 1, 11] =   11 positive integers

 

 

 

cool cool cool

 Apr 26, 2019

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