x^2 + 2x - 15 = (x+5)(x-3)
If m > 0, then -m < 0.
Question stem, rephrased:
What is the probability that (x+5)(x-3) < 0 ?
We can use the CRITICAL POINT APPROACH.
Critical points occur when the two sides of the inequality are EQUAL.
In the inequality above, the left side is equal to 0 when x=-5 or x=3.
To determine which ranges satisfy the inequality, test one value to the left and one value to the right of each critical point.
Here, we must test x<-5, -5<x<3 and x>3.
If we test x=-10, x=0, and x=10, only x=0 satisfies (x+5)(x-3) < 0.
Implication:
-5<x<3 is the only valid range.
Thus:
Of the 21 integers between -10 and 10, inclusive, only the 7 integers between between -5 and 3
satisfy (x+5)(x-3) < 0, yielding the following probability:
7/21 = 1/3
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