What is the smallest integer that satisfies the inequality (x - 3)/ (x^2 - 8x - 20) > 0> 0?
Choose the correct choice:
A) -2	B) 10	C) 3	D) -1	E) 0
Explanatory Answer   Let us factorize the denominator and rewrite the expression as x−3 /(x−10)(x+2) &gt; 0   Equate each of the terms of the expression to zero to identify the values of x that are relevant to test whether the inequality holds good.   The values that are relevant to us are x = 3, x = 10 and x = -2.   Let us arrange these values in ascending order: -2, 3 and 10.   The quickest way to solve inequalities questions after arriving at these values is verifying whether the inequality holds good at the following intervals.   Interval 1: x &lt; -2.   Pick a value in that range and check whether the inequality holds good.   Let us take x = -10. When x = -10, x−3 /(x−10)(x+2) &lt; 0; the inequality DOES NOT hold good in this interval.   Interval 2: -2 &lt; x &lt; 3.   Let us take x = 0. When x = 0, x−3/(x−10)(x+2) = 0−3 /(0−10)(0+2) &gt; 0; the inequality holds good in this interval.   The least integer value that x can take if x &gt; -2 is x = -1.   So, the correct answer is -1. Choice D.   Remember: We have to find out the least integer value. And we have arrived at -1.   Do, not waste time computing the entire range of values of x that satisfy the inequality.   Note: In any inequality question, when the question asks us to determine the intervals in which the inequality holds good, we have to eliminate values of x that will result in the denominator becoming zero.   Choice -1
<result>D</result>
What is the smallest integer that satisfies the inequality (x - 3)/ (x^2 - 8x - 20) > 0> 0?