question_answer

The value of x for which\[|x+3|>|2x-1|\]is

A)  \[\left( -\frac{2}{3},4 \right)\]

B)  \[\left( \frac{-2}{3},\infty  \right)\]

C)  (0,1)              

D)  None of these

Correct Answer: A

Solution :

 \[|x+3|>|2x-1|\] \[\Rightarrow \] \[|x+3{{|}^{2}}>|2x-1{{|}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+9+6x>4{{x}^{2}}+1-4x\] \[\Rightarrow \] \[3{{x}^{2}}-10x-8<0\] \[\Rightarrow \] \[(x-4)(3x+2)<0\]