SOLUTION: An integer is such that half of the next integer is at least 4 more than one-third of the previous integer. Find the least value of the integer.

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Question 662241: An integer is such that half of the next integer is at least 4 more than one-third of the previous integer. Find the least value of the integer.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Let the integer = N

Next integer = N+1

Previous integer = N-1

Half the next integer = %28N%2B1%29%2F2

One third the previous integer = %28N-1%29%2F3 

%28matrix%285%2C1%2C%0D%0A%0D%0AHalf%2Cof%2Cthe%2Cnext%2Cinteger%29%29 ≧ %28matrix%286%2C1%2C%0D%0A%0D%0AOne%2Cthird%2Cof%2Cthe%2Cprevious%2Cinteger%29%29 + 4

    %28N%2B1%29%2F2 ≧  %28N-1%29%2F3 + 4 

  3(N+1) ≧ 2(N-1) + 24

    3N+3 ≧ 2N-2 + 24

       N ≧ 19
    
19 is the least possible value of N

Edwin