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Find the range of values of x such that ((x-3)(x-4))/((x+1)(x+2))>0

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Find the range of values of x such that ((x-3)(x-4))/((x+1)(x+2))>0  [#permalink]

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New post Updated on: 31 Aug 2018, 01:06
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A
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E

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  35% (medium)

Question Stats:

64% (01:14) correct 36% (01:55) wrong based on 107 sessions

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Solving inequalities- Number Line Method - Practice Question #3

Find the range of values of x such that \(\frac{((x-3)(x-4))}{((x+1)(x+2))>0}\)


A. x > 4
B. (-1 ,4)
C. (-2, -1) U (3,4)
D. (-1,3) U (4, +inf)
E. (-inf, -2) U (-1, 3) U (4, +inf)

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Originally posted by EgmatQuantExpert on 23 Aug 2018, 03:29.
Last edited by EgmatQuantExpert on 31 Aug 2018, 01:06, edited 2 times in total.
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Re: Find the range of values of x such that ((x-3)(x-4))/((x+1)(x+2))>0  [#permalink]

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New post Updated on: 27 Aug 2018, 01:10

Solution


Given:
    An inequality, \(\frac{(x-3)(x-4)}{(x+1)(x+2)}>0\)

To find:
    The range of x, that satisfies the above inequality

Approach and Working:
    The first step is to multiply the inequality by (x+1)^2 and (x+2)^2 on both sides
    Thus, we get,
      \(\frac{(x+1)^2 (x+2)^2 (x-3)(x-4))}{((x+1)(x+2)}>0\)
      Which implies, (x + 1) * (x + 2) * (x - 3) * (x - 4) > 0, and x ≠ {-1, -2}, since the denominator cannot be zero.
    The zero points of this inequality are, x = -2, x = -1, x = 3, x = 4
    Plot these points on the number line.
      Since, 4 is the greatest among all, the inequality will be positive, for all the points to the right of 4, on the number line
      And, it is negative, in the region, between 3 and 4
      It is again positive in the region, between -1 and 3
      And, it is again negative in the region, between -2 and -1
      And, it is positive for all the values less than -2

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Therefore, the range of x is x > 4 and -1 < x < 3 and x < -2

Hence, the correct answer is option E.

Answer: E

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Originally posted by EgmatQuantExpert on 23 Aug 2018, 03:32.
Last edited by EgmatQuantExpert on 27 Aug 2018, 01:10, edited 2 times in total.
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Re: Find the range of values of x such that ((x-3)(x-4))/((x+1)(x+2))>0  [#permalink]

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New post 23 Aug 2018, 05:13
EgmatQuantExpert wrote:
Solving inequalities- Number Line Method - Practice Question #3

Find the range of values of x such that \(\frac{((x-3)(x-4))}{((x+1)(x+2))>0}\)


A. x > 4
B. (-1 ,4)
C. (-2, -1) U (3,4)
D. (-1,3) U (4, +inf)
E. (-inf, -2) U (-1, -3) U (4, +inf)


\(\frac{((x-3)(x-4))}{((x+1)(x+2))>0}\)

using wavy curve method:-

x<-2 or -1<x<3 or x>4.

So, ranges of x in interval form: (-inf, -2) U (-1, -3) U (4, +inf)

Ans. (E)
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Re: Find the range of values of x such that ((x-3)(x-4))/((x+1)(x+2))>0  [#permalink]

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New post 30 Aug 2018, 22:56
E. (-inf, -2) U (-1, -3) U (4, +inf)

-3 must be changed to 3
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Re: Find the range of values of x such that ((x-3)(x-4))/((x+1)(x+2))>0  [#permalink]

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New post 30 Aug 2018, 23:00
soleimanian wrote:
E. (-inf, -2) U (-1, -3) U (4, +inf)

-3 must be changed to 3


Hi soleimanian,
You have pointed out correctly.

Hi EgmatQuantExpert,
Hope you will do the needful.
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Re: Find the range of values of x such that ((x-3)(x-4))/((x+1)(x+2))>0  [#permalink]

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New post 31 Aug 2018, 01:08
Hey soleimanian,
Apology for the typo.

We have updated the option.
Regards,
Ashutosh
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Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
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Re: Find the range of values of x such that ((x-3)(x-4))/((x+1)(x+2))>0 &nbs [#permalink] 31 Aug 2018, 01:08
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