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B
(−∞,−72)
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C
(−∞,−3)
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D
(−16,8)
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Solution
The correct option is C(−∞,−72) Given, |9−x|<2−3x Case 1: When 9−x>0⇒|9−x|=9−x Then, 9−x<2−3x ⇒2x<−7 ⇒x<−72 -- (1) Case 2: When 9−x<0⇒|9−x|=−(9−x) Then, −9+x<2−3x ⇒4x<11 ⇒x<112 --- (2) From, solutions 1,2, we get ⇒x<−72 or (−∞,−72)