If (x-11)(x-3) < 0, which of the following must be true?  Answers
A) x^2 + 5x + 6 < 0 B) x^2 + 5x + 6 > 0 C) 5 - x < 0 D) x - 5 < 0 E) 11 - x > 0
(x-11)(x-3) &lt; 0; 3<x<11 --=""> Given condition   If we review options, E is always true.   Let us review others:   x^2 + 5x + 6 </x<11>= (x+3)(x+2)   (x+3)(x+2)&lt;0, then -3<x<-2 --=""> This will not be true with the given conditions (3&lt;x&lt;11). A is out   x^2 + 5x + 6 </x<-2>= (x+3)(x+2)   (x+3)(x+2)&gt;0, then x&gt; -2 and x &lt; -3 --&gt; This will not be true with the given conditions (3<x<11). (c)="" -="" 0;="" 5="" 5<x;="" <="" b="" is="" out="" x=""> 5. But if x </x<11).>= 12 , then given condition is not satisfied. So C is also out.   D. x - 5 &lt; 0   x&lt;5   But if x = 1, (which is less than 3) then given condition is not satisfied.   11 - x &gt; 0 is the answer.
<result>E</result>
If (x-11)(x-3) < 0, which of the following must be true?