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Find the range of values of x such that ((x3)(x4))/((x+1)(x+2))>0
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Updated on: 16 Dec 2018, 10:01
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Solving inequalities Number Line Method  Practice Question #3Find the range of values of x such that \(\frac{(x3)(x4)}{(x+1)(x+2)}>0\) 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) Previous Question  Next QuestionTo read the article: Solving inequalities Number Line MethodTo read all our articles:Must Read articles to reach Q51
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Originally posted by EgmatQuantExpert on 23 Aug 2018, 04:29.
Last edited by Bunuel on 16 Dec 2018, 10:01, edited 3 times in total.



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Re: Find the range of values of x such that ((x3)(x4))/((x+1)(x+2))>0
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Updated on: 27 Aug 2018, 02:10
Solution Given: An inequality, \(\frac{(x3)(x4)}{(x+1)(x+2)}>0\) 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,
\(\frac{(x+1)^2 (x+2)^2 (x3)(x4))}{((x+1)(x+2)}>0\) 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. Answer: E
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Re: Find the range of values of x such that ((x3)(x4))/((x+1)(x+2))>0
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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 \(\frac{((x3)(x4))}{((x+1)(x+2))>0}\)
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)
\(\frac{((x3)(x4))}{((x+1)(x+2))>0}\) 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 ((x3)(x4))/((x+1)(x+2))>0
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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 ((x3)(x4))/((x+1)(x+2))>0
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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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Re: Find the range of values of x such that ((x3)(x4))/((x+1)(x+2))>0
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31 Aug 2018, 02:08
Hey soleimanian, Apology for the typo. We have updated the option. Regards, Ashutosh eGMAT
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Re: Find the range of values of x such that ((x3)(x4))/((x+1)(x+2))>0
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16 Dec 2018, 09:48
EgmatQuantExpert wrote: Solving inequalities Number Line Method  Practice Question #3Find the range of values of x such that \(\frac{((x3)(x4))}{((x+1)(x+2))>0}\) 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) Previous Question  Next QuestionTo read the article: Solving inequalities Number Line MethodTo read all our articles:Must Read articles to reach Q51 Dear Moderator, Can we format the question properly, seems as though only the denominator, is > 0, Thank you.
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Re: Find the range of values of x such that ((x3)(x4))/((x+1)(x+2))>0
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16 Dec 2018, 10:01
stne wrote: EgmatQuantExpert wrote: Solving inequalities Number Line Method  Practice Question #3Find the range of values of x such that \(\frac{((x3)(x4))}{((x+1)(x+2))>0}\) 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) Previous Question  Next QuestionTo read the article: Solving inequalities Number Line MethodTo read all our articles:Must Read articles to reach Q51 Dear Moderator, Can we format the question properly, seems as though only the denominator, is > 0, Thank you. ______________ Done. Thank you.
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Re: Find the range of values of x such that ((x3)(x4))/((x+1)(x+2))>0
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16 Dec 2018, 10:01






