A) infinite
B) two solutions
C) three sollutionns
D) no solutions
Correct Answer: A
Solution :
[a] Let\[2(2x+3)-10<6(x-2)~\ldots (1)\] |
\[\frac{2x-3}{4}+6\ge \frac{2+4x}{3}~\ldots (2)\] |
\[(1)\Rightarrow 4x+6-10-6x+12<0\] |
\[\Rightarrow -2x+8<0\] |
\[\Rightarrow -2x<-8\Rightarrow x>4\,\,i.e.,x\in (4,\infty )\] |
\[(2)\,\,\Rightarrow \frac{2x-3+24}{4}\ge \frac{2+4x}{3}\] |
\[\Rightarrow 6x+63\ge 8+16x\] |
\[\Rightarrow 6x-16\ge 8-63\] |
\[\Rightarrow -10x\ge -55\] |
\[\Rightarrow x\le \frac{55}{10}i.e.,x\in \left( -\infty ,\frac{55}{10} \right]\] |
Solution set is given by \[\left( -\infty ,\frac{55}{10} \right]\cap (4,\infty )=\left( 4,\frac{55}{10} \right]\] |
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