Linear Programming Question 33
Question: Solution set of the inequality $ 6\le -3(2x-5)<12 $ is
Options:
A) $ (0,3/2) $
B) $ ( 1/2,3/2 ] $
C) $ [ 1/2,3/2 ) $
D) $ [ 0,1/2 ) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ 6\le -3(2x-5)<12 $
$ \Rightarrow 2\le -(2x-5)<4 $
$ \Rightarrow -2\ge 2x-5>-4 $
$ \Rightarrow 5-2\ge 2x>5-4 $
$ \Rightarrow 3\ge 2x>1 $
$ \Rightarrow 3/2\ge x>1/2 $
Thus, the solution set for the given inequality is (1/2, 3/2].
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