The solution set for the inequality |x+2| < |4x+1|
(a) -3/5 < x < 1/3
(b) -1/3 < x < 3/5
(c) 0 < x < 1/3
(d) -1/3 < x < 1/3
(e) None of these
Correct Answer: (E)
Explanation
Since the expressions on both sides of the inequality are under modulus, you can square on both sides without disturbing the inequality.
(x+2)2 < (4x+1)2
x2 + 4x + 4 < 16x2 + 8x + 1
15x2 + 4x – 3 > 0
(5x + 3)(3x – 1) > 0
Hence, x € (-∞, -3/5) U (1/3, +∞)