If x is a positive integer and (x - 9)(x + 5)/(x - 7)

Question

If  x  is a positive integer and  \frac{(x-9)(x+5)}{(x-7)} \leq 0 , how many values are possible for  x ?

A. 1
B. 2
C. 3
D. 4
E. 0

Snehaaaaa · Answer

Explanation-
 \frac{(x-9)(x+5)}{(x-7)} \leq 0 
Multiply and divide by  (x-7)^{2} 
 (x-9)(x+5)(x-7) \leq 0 
Equating with zero, we get zero points as --> 9, -5, 7
We will remove 7 from the possible values for x as the denominator is  (x-7)  
Therefore, possible values of x are -5 and 7

Correct Answer is (B)

AlevtinaN · Answer

X should be a positive integer. 
And x should be 7 < X <= 9 
So it’s 8 and 9 - answer B

Posted from my mobile device

Sourav23 · Answer

can it be solved by wavey curve method??

Bunuel · Answer

We have: \frac{(x-9)(x+5)}{(x-7)} ≤ 0 The transition points are x = -5 , x = 7 , and x = 9 (these are the values of x at which expression changes the sign). This gives us four ranges: x ≤ -5 -5 < x < 7 7 < x ≤ 9 x > 9 Next, test an extreme value for x: if x is a large enough number, say 100, then both the numerator and denominator will be positive, resulting in a positive value for the whole expression. Therefore, when x > 9, the expression is positive. Now, here’s the trick: since the expression is positive in the 4th range, it will be negative in the 3rd range, positive again in the 2nd range, and negative in the 1st range, following the pattern: -, +, -, +. Thus, the expression is negative (or 0) for -5 ≤ x < 7 and 7 < x ≤ 9 . Since given that x is a positive integer x can only be 8 or 9. Answer: B.

Sourav23 · Answer

Thanks mate. cheers

If x is a positive integer and (x - 9)(x + 5)/(x - 7) < 0, how many

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