A) \[\left( -\infty ,-\frac{1}{3} \right)\cup \left[ \frac{1}{4},\infty \right)\]
B) \[\left( -\infty ,-\frac{2}{3} \right)\cup \left[ \frac{1}{5},\infty \right)\]
C) \[\left( -\infty ,-\frac{1}{3} \right)\cup \left[ 2,\infty \right)\]
D) \[\left( -\infty ,-\frac{2}{3} \right)\cup \left[ 4,\infty \right)\]
E) \[\left( -\infty ,-\frac{1}{3} \right)\cup \left[ \frac{1}{2},\infty \right)\]
Correct Answer: C
Solution :
Given inequality is\[\frac{4x-1}{3x+1}\ge 1\] \[\Rightarrow \]\[\frac{4x-1}{3x+1}-1\ge 0\]\[\Rightarrow \]\[\frac{x-2}{3x+1}\ge 0\] \[\Rightarrow \]\[x-2\ge 0\]and\[3x+1>0\] Or \[x-2\le 0\]and\[3x+1<0\] \[\Rightarrow \]\[x\ge 2\] or \[x<-\frac{1}{3}\] \[\Rightarrow \]\[x\in \left( -\infty ,-\frac{1}{3} \right)\cup (2,\infty )\]
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