Question 30152
x^2+5x>24
That is x^2+5x-24 > 0
(x+8)(x-3) > 0
Since either positive multiplied by positive is positive OR
negative multiplied by negative is positive, there are two cases.
Case 1: Let (x+8) > 0 together with (x-3) > 0
This implies x > -8 together with x > 3
And since anything to the right of 3 is definitely to the right of (-8), 
the verdict for this case is 
x > 3 
Case 2: Let (x+8) < 0 together with (x-3) < 0
This implies x < -8 together with x < 3
And since anything to the left of (-8) is definitely to the left of 3, 
the verdict for this case is 
x < -8
Therefore combining the results of both the cases we have 
Answer:  x< -8 and x > 3
Which is your choice (d) 
Note: (factoring the quadratic expression: x^2+5x-24,
product =(-24) and sum is 5 and therefore the quantities are (+8) and (-5)
and therefore x^2+5x-24
= x^2+(8x-3x)-24
= (x^2+8x)-3x-24
=x(x+8)-3(x+8)
=xp-3p  where p = (x+8)
=p(x-3)
=(x+8)(x-3)