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Which of the following inequalities have a finite range of values of x
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Updated on: 10 Apr 2015, 02:47
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Which of the following inequalities have a finite range of values of x satisfying them? A. x^2 + 5x + 6 > 0 B. x + 2 > 4 C. 9x  7 < 3x + 14 D. x^2  4x + 3 < 0
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Originally posted by Eden on 03 Sep 2010, 06:09.
Last edited by Bunuel on 10 Apr 2015, 02:47, edited 1 time in total.
Renamed the topic and edited the question.




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Re: Which of the following inequalities have a finite range of values of x
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03 Sep 2011, 19:57
MBAhereIcome wrote: 1. x^2 + 5x + 6 >0 => (x+2)*(x+3)>0 => x>2 or x<3
why x<3? what is wrong with the below? x+3>0 x>3 (x+2)*(x+3)>0 does not mean (x+3)>0 You have to work with both the terms simultaneously. When will the product of (x+2) and (x+3) be positive? When either both (x+2) and (x+3) are positive or both (x+2) and (x+3) are negative. Both positive x+2 > 0 x > 2 and x+3 > 0 x > 3 In this case, x must be greater than 2 OR Both negative x+2 < 0 x < 2 and x+3 < 0 x < 3 In this case, x must be less than 3. So either x > 2 OR x < 3. If you want to avoid all this work, look at this post by gurpreet singh: inequalitiestrick91482.html?hilit=inequalities%20trick
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Re: Which of the following inequalities have a finite range of values of x
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03 Sep 2010, 06:53
Lets get started with this, choice by choice:
Choice I: x^2 + 5x + 6 > 0 Break this one: (x+2)(x+3) > 0. So either x>2 or x<3 So infinite values of x.
Choice II:x + 2 > 4 Break this one: either x+2>4 or x+2<4 i.e x>2 or x<6 So infinite values of x.
Choice III:9x  7 < 3x + 14 Break this one: x< 3.33 So infinite values of x.
Choice IV:x^2  4x + 3 < 0 Break this one: (x3)(x1)<0. So x is between 1<x<3 So here x have finite values.
Hence answer is D




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Re: Which of the following inequalities have a finite range of values of x
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03 Sep 2010, 06:53
A. X^2 + 5X >6 you can see that X can be all positive including 0 so not finite B. this shows X has to be >3 and <7 so again not finite C. move terms around gets 6x < 21 so x can be any negative value and couple of positives so infinite D. x^2  4x <3 You can readily see that X cant be negative since the 4X and x^2 results in positives thus invalidates the inequality. Try plugin couple of numbers  0 doesnt work since 0<3 is invalid. X=1 gets you 3<3 so no. x=2 gets you 48 = 4<3 which works x=3 gets 912=3 <3 so no. Stop here and you see x can be only 2 so D
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Re: Which of the following inequalities have a finite range of values of x
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04 Aug 2011, 13:39
Which of the following inequalities have a finite range of values of "x" satisfying them? 1.x^2 + 5x + 6 > 0 2.x + 2 > 4 3.9x  7 < 3x + 14 4.x^2  4x + 3 < 0
well i have seen that Q and answered correctly, but the suggestes solution for denying the 1st answer was: Evaluating both the options, we get the range of values of "x" that satisfy this inequality to be x < 2 or x > 3. i.e., "x" does not lie between 2 and 3 or an infinite range of values.
after reading Fluke's, Karishma's and Bunuel's posts i thought inequalities are clearer. though in my decent opinion that the answer should be x>2 and x<3.
correct me if i am wrong



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Re: Which of the following inequalities have a finite range of values of x
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04 Aug 2011, 15:58
Lets try and solve this one by one, dimri10. 1. x^2 + 5x + 6 >0 => (x+2)*(x+3)>0 => x>2 or x<3 You are right about the range of values here. The answer is x>2 and x<3. Lets test with a couple of values. Putting x=4 (<3) here we get a positive answer. Putting x=1 (>2) here we again get a positive answer. Putting x=2.5 here we get a negative answer. Confirmed. The answer to this option is therefore not a finite range of values. 2. x+2 > 4 => x > 2 and x < 6 Again, not a finite range of values. 3. 9x  7 < 3x + 14 => x < 21/6 => x < 7/2 A range, and not a finite range of values. 4. x^2  4x + 3 < 0 => (x1)*(x3) < 0 => x>1 and x<3 This is a finite range of values. The answer is therefore (4).
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Re: Which of the following inequalities have a finite range of values of x
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05 Aug 2011, 07:40
for the first one the solution is x>2 or x<3 , not and. So we have two cases . if you consider either one of the case, its not yielding a finite range. 4th is the only option that can yield finite range solution. hence 4th choice is correct. dimri10 wrote: Which of the following inequalities have a finite range of values of "x" satisfying them? 1.x^2 + 5x + 6 > 0 2.x + 2 > 4 3.9x  7 < 3x + 14 4.x^2  4x + 3 < 0
well i have seen that Q and answered correctly, but the suggestes solution for denying the 1st answer was: Evaluating both the options, we get the range of values of "x" that satisfy this inequality to be x < 2 or x > 3. i.e., "x" does not lie between 2 and 3 or an infinite range of values.
after reading Fluke's, Karishma's and Bunuel's posts i thought inequalities are clearer. though in my decent opinion that the answer should be x>2 [strike]and[/strike]x<3.
correct me if i am wrong



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Re: Which of the following inequalities have a finite range of values of x
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05 Aug 2011, 11:43
4 alone .. x^2  4x + 3 < 0 (x1)*(x3) < 0 x>1 and x<3



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Re: Which of the following inequalities have a finite range of values of x
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03 Sep 2011, 10:13
1. x^2 + 5x + 6 >0 => (x+2)*(x+3)>0 => x>2 or x<3 why x<3? what is wrong with the below? x+3>0 x>3
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Re: Which of the following inequalities have a finite range of values of x
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26 Dec 2011, 15:36
MBAhereIcome wrote: 1. x^2 + 5x + 6 >0 => (x+2)*(x+3)>0 => x>2 or x<3
why x<3? what is wrong with the below? x+3>0 x>3 I think you cannot divide that inequality by \((x+2)\) or \((x+3)\) to isolate \(x\). You don't know if they are positive or negative. +1 D
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Re: Which of the following inequalities have a finite range of values of x
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26 Dec 2011, 17:02
Thanks @Karishma and @Gurupreet singh.........................Very useful post It should be D
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Re: Which of the following inequalities have a finite range of values of x
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27 Dec 2011, 02:48
well explained by karishma . Thanks



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Re: Which of the following inequalities have a finite range of values of x
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09 Apr 2015, 20:08
I solved this by graphic approach like it has been suggested on other posts. you find the roots, draw the first two parabolas and x=21/6 and you realize that region isn't bound. The last one has roots 3 and 1, but is <0, so is bound.



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Re: Which of the following inequalities have a finite range of values of x
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10 Apr 2015, 02:49



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Re: Which of the following inequalities have a finite range of values of x
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01 Dec 2018, 07:09
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Re: Which of the following inequalities have a finite range of values of x &nbs
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