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Given inequality is:
7 < (3x+11)/2 < 11
=> 7*2 < 3x+11 < 11*2
=> 14 < 3x+11 < 22
=> 14-11 < 3x < 22-11
=> 3 < 3x < 11
=> 3/3 < x < 11/3
=> 1 < x < 11/3