How many integer values of x do NOT satisfy (x–4)(x+3)/(x+4)(x+5) 0?

Question

How many integer values of x do NOT satisfy  \frac{(x–4)(x+3)}{(x+4)(x+5)} > 0 ?

A. 11
B. 10
C. 9
D. 8
E. 7

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Kinshook · Answer

Asked: How many integer values of x do NOT satisfy  \frac{(x–4)(x+3)}{(x+4)(x+5)} > 0 ?

\frac{(x–4)(x+3)}{(x+4)(x+5)} < 0 
when -3<=x<=4; 8 values
and when -5<x<-4; 2 values

IMO B

TestPrepUnlimited · Answer

We would like to scrutinize the range x <= 4 and x >= -5 . When x > 4 , we have all four factors as positive and the fraction must be greater than 0. When we have x < -5 , all four factors are negative and the fraction must be greater than 0. Then our focus is the range -5 <= x <= 4 , the four values x = 4, -3, -4, -5 either make the fraction 0 or create the divide by 0 error. The values of x between (x = 4) and (x = -3), -2 <= x <= 3 give 3 positive terms and 1 negative term, making the fraction negative so we include all those values too. In total, we have 4 + 6 = 10 values that do not satisfy this inequality. Ans: B

ajaykv · Answer

multiply both sides by (x+4)^2 (x+5)^2
u get (x-4)(x+3)(x+4)(x+5) > 0
using the number line method. We can identify that -2,-1,0,1,2,3 all give negative values hence less than 0.
Also -4,-3,-5 and 4 makes the equation equal to 0.
so total is 10 values.
IMO B

https://gmatclub.com/forum/solving-ineq ... 74110.html

PallabiKundu · Answer

B should be the answer (10 values) ranging from -5 to +4 (inclusive)
 Bunuel  can u please clarify?

ScottTargetTestPrep · Answer

We see that if x is an integer greater than 4, all the factors are positive; therefore, the expression is positive and hence greater than 0. Similarly, if x is an integer less than -5, all the factors are negative; therefore, the expression is positive and hence greater than 0. Therefore, all the values of x that do not satisfy the inequality must be between -5 and 4, inclusive.

Even though -4 and -5 make the denominator 0, they are still values of x that do not allow the given inequality to hold as true. Thus, these two values are counted.. Furthermore, if x is 4 or -3, we see that the numerator will be 0, which makes the entire expression 0. Since 0 is not greater than 0, we will include 4 and -3 as two additional values of x that do not allow the given equality to hold as true.

Finally, we see that if x is any integer value from -2 to 3, inclusive, (x - 4) will be negative, while the other 3 factors, (x + 3), (x + 4) and (x + 5) will be positive. Therefore, the value of the expression is negative, and hence it’s not greater than 0 for any of these six values of x.

Therefore, there are 2 + 2 + 6 = 10 integer values of x that do not satisfy the inequality. They include all integers between -5 and 4, inclusive.

Answer: B

AnkithaSrinivas · Answer

How can we consider if the value is undefined?

Gaurav2896 · Answer

I think answer is clearly 8 not 10 because , for -4 and -5 , if you substitute in equation we get ( something/0 ) , any mathematic person can say this will tends to infinity , (for ex 1/0 = tends to infinity by concept of limits) , so LHS > 0 is sustained , so answer should be only 8 i.e -3,-2,-1,0,1,2,3,4 .
 Bunuel  i thinnk OA should be fixed.

ishwan · Answer

VeritasKarishma  Can you please help me to understand this question ?

KarishmaB · Answer

Normally, the questions we see are like this: For how many integer values of x, is \frac{(x–4)(x+3)}{(x+4)(x+5)} > 0 ? Here, the questions says "how many integer values DO NOT satisfy..." So we can find the values that satisfy the inequality: \frac{(x–4)(x+3)}{(x+4)(x+5)} > 0 and our answer would be the complementary set of that. So we find the integer values for which the expression: \frac{(x–4)(x+3)}{(x+4)(x+5)} is positive and for all other integer values of x, this expression will not be positive. It could be negative, 0 or not defined for those values. \frac{(x–4)(x+3)}{(x+4)(x+5)} > 0 Using the wavy line method, we see that x > 4 or -4 < x < -3 or x < -5. So the integer values for which the inequality holds are x = 5, 6, 7, ... infinity x = - infinity, ... -7, -6 Hence for all integer values between -5 to 4 (inclusive), the inequality does not hold. So for all these values, the given expression is not positive. It may be 0 or it may be negative or it may not be defined. For these 10 values (from -5 to 4), the expression is not positive. Answer (B) ishwan

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How many integer values of x do NOT satisfy (x–4)(x+3)/(x+4)(x+5) > 0?

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