Asked: Which of the following inequalities is equal to |x-3|x||<8?
|x-3|x||<8
-8 <x - 3|x| < 8
Case 1: x>0
-8 < x - 3x < 8
-8 < -2x < 8
-4< x < 4
Since x>0
0 < x < 4
Case 2: x<=0
-8 < x+3x < 8
-8 < 4x < 8
-2 < x < 2
Since x<=0
-2 < x <=0
Combining above 2:
-2 < x < 4
IMO C
|x-3|x||<8
-8 <x - 3|x| < 8
Case 1: x>0
-8 < x - 3x < 8
-8 < -2x < 8
-4< x < 4
Since x>0
0 < x < 4
Case 2: x<=0
-8 < x+3x < 8
-8 < 4x < 8
-2 < x < 2
Since x<=0
-2 < x <=0
Combining above 2:
-2 < x < 4
IMO C
