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}x

^{2}+ 4x + 4 < 16x^{2}+ 8x + 115x

^{2}+ 4x – 3 > 0(5x + 3)(3x – 1) > 0

Hence, x € (-∞, -3/5) U (1/3, +∞)

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