Lets try and solve this one by one, dimri10.
1. x^2 + 5x + 6 >0
=> (x+2)*(x+3)>0
=> x>-2 or x<-3
You are right about the range of values here. The answer is x>-2 and x<-3. Lets test with a couple of values. Putting x=-4 (<-3) here we get a positive answer. Putting x=-1 (>-2) here we again get a positive answer. Putting x=-2.5 here we get a negative answer. Confirmed. The answer to this option is therefore not a finite range of values.
2. |x+2| > 4
=> x > 2 and x < -6
Again, not a finite range of values.
3. 9x - 7 < 3x + 14
=> x < 21/6
=> x < 7/2
A range, and not a finite range of values.
4. x^2 - 4x + 3 < 0
=> (x-1)*(x-3) < 0
=> x>1 and x<3
This is a finite range of values.
The answer is therefore (4).
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