Question

Which of the following is the solution to | x -12 | < 15

Answer 1

Hello,
Answer D    -3<x<27
Indeed:
1)
if x-12≥0 then x≥12 and
|x-12|=x-12x-12<15 → x<27
so 12≤x<27
2) if x-12<0 then
x<12 and|x-12|=-(x-12)<15
-x+12<15-x<3 → x>-3
So -3<x<12
Thus -3<x<12  U 12≤x<27 ⇔ -3<x<27