Question

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

Answer 1

Rezolvam inecuatia ;
6I2x-5I + 12x-33 < 15x+35 -3x -12
6I3x-5I +12x -33 < 12x + 23
6I3x-5I < 56 /÷2
3I3x-5I < 28
I9x-15I < 28 ⇒ -28 <9x-15 < 28 /+15
-13 <9x <43 /÷9 ⇒
-13/9 < x < 43/9 ⇒  x∈{-1,1,2,3,4}

Answer 2

6|2x-5|+12x-33)<15x+35-3x-12
6|2x-5|+12x-33<12x+23
6|2x-5|+12x-12x<23+33
6|2x-5|<56
|2x-5|<56/6
|2x-5|<28/3
-28/3<2x-5/28/3
-28<6x-15<28 |+15
-13<6x<43 |+13
6x<56
x<56/6
x<28/3
x<9,(3)=>x aparține {..., -1, 1, 2, 3, ..., 9}

A={..., -1, 1, 2, 3, ..., 9}