Question

A={x€Z* | 3(2|2x-5| +4x-11)<5(3x+7)-3x-12}

Answer 1

3(2|2x-5| +4x - 11) < 5(3x+7) -3x-12
ptr. 2x-5 ≥ 0    (x ≥ 5/2)   |2x-5| = 2x-5
3(4x - 10 +4x-11) < 15x +35 - 3x -12
12x < 96   x < 8      3 ≤ x < 8     x∈[3,4,5,6,7]
ptr. 2x-5 < 0   (x <5/2)    |2x-5| = 5 - 2x
3(10-4x +4x -11) < 12x + 23       12 x > - 26   x > - 13/6  ⇒ x∈[-2,-1,1,2.....+∞)
A = [3,4,5,6,7] ∩ [-2.-1,1,2,.....) = [3,4,5,6,7]
ex. x = 3   3·3 < 80 - 21     9 < 59