A) \[(4,\,\infty )\cup \left( -\infty ,\,0 \right]\]
B) \[[4,\,\infty ]\cup \left( -\infty ,\,4 \right]\]
C) \[\left( -\infty ,\,0 \right]\cup (4,\,\infty )\]
D) \[[4,\,\infty ]\cup \left( -\infty ,\,0 \right]\]
Correct Answer: C
Solution :
[c] \[\frac{5x+8}{4-x}\le 2\Rightarrow \frac{5x+8}{4-x}-2\le 0\] \[\Rightarrow \frac{5x+8-8+2x}{4-x}\le 0\] \[\Rightarrow \frac{7x}{4-x}\le 0\Rightarrow \frac{x-0}{x-4}\ge 0\] Dividing by -7 \[\Rightarrow (-\infty ,0]\cup (4,\infty )\]
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