Linear Programming Question 127
Question: The solution set of $ \frac{5x+8}{4-x}\le 2 $ is
Options:
A) $ (4,\infty )\cup ( -\infty ,0 ] $
B) $ [4,\infty ]\cup ( -\infty ,4 ] $
C) $ ( -\infty ,0 ]\cup (4,\infty ) $
D) $ [4,\infty ]\cup ( -\infty ,0 ] $
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Answer:
Correct Answer: C
Solution:
$ \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 ) $
BETA
