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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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Updated on: 31 Aug 2018, 02:06
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45% (medium)

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60% (01:06) correct 40% (01:59) wrong based on 85 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, 04:29.
Last edited by EgmatQuantExpert on 31 Aug 2018, 02:06, edited 2 times in total.
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Joined: 04 Jan 2015
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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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Updated on: 27 Aug 2018, 02:10

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

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

Hence, the correct answer is option E.

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Originally posted by EgmatQuantExpert on 23 Aug 2018, 04:32.
Last edited by EgmatQuantExpert on 27 Aug 2018, 02:10, 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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23 Aug 2018, 06:13
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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30 Aug 2018, 23:56
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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31 Aug 2018, 00:00
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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PKN

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Joined: 04 Jan 2015
Posts: 1995
Re: Find the range of values of x such that ((x-3)(x-4))/((x+1)(x+2))>0  [#permalink]

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31 Aug 2018, 02:08
Hey soleimanian,
Apology for the typo.

We have updated the option.
Regards,
Ashutosh
e-GMAT
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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, 02:08
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