Equations And Inequalities Question 32
Question: Solution of $ | 2x-3 |<| x+2 | $ is
Options:
A) $ ( -\infty ,\frac{1}{3} ) $
B) $ ( \frac{1}{3},5 ) $
C) $ (5,\infty ) $
D) $ ( -\infty ,\frac{1}{3} )\cup (5,\infty ) $
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ | 2x-3 |<| x+2 | $
$ \Rightarrow -| x+2 |<2x-3<| x+2 | $ ? (i) Case I: $ x+2\ge 0. $ Then by (i), $ -(x+2)<2x-3<x+2 $
$ \Rightarrow -x-2<2x-3<x+2 $
$ \Rightarrow 1<3xandx<5\Rightarrow \frac{1}{3}<x<5 $
Case II: $ x+2<0. $ Then by (i),
$ (x+2)<2x-3<-(x+2) $
$ \Rightarrow -(x+2)>2x-3>(x+2) $
$ \Rightarrow 1>3x $ and $ x>5\Rightarrow \frac{1}{3}\le x $ and $ x>5, $ not possible.
BETA
