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# Help

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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

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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

Apr 26, 2019