Which of the following inequalities have a finite range of values of x

Question

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

optimisticAL · Accepted Answer

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: (x-3)(x-1)<0. So x is between 1<x<3
So here x have finite values.

Hence answer is D

KarishmaB · Answer

(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: inequalities-trick-91482.html?hilit=inequalities%20trick

shaselai · Answer

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 4-8 = -4<-3 which works x=3 gets 9-12=-3 <-3 so no. Stop here and you see x can be only 2

so D

dimri10 · Answer

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

GyanOne · Answer

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
=> (x-1)*(x-3) < 0
=> x>1 and x<3
This is a finite range of values.

The answer is therefore (4).

Spidy001 · Answer

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.

gladvijay · Answer

4 alone .. 
 x^2 - 4x + 3 < 0
 (x-1)*(x-3) < 0
 x>1 and x<3

MBAhereIcome · Answer

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

metallicafan · Answer

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

mydreammba · Answer

Thanks @Karishma and @Gurupreet singh.........................Very useful post

It should be D

sandeeepsharma · Answer

well explained by karishma . Thanks

nphatak · Answer

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.

Bunuel · Answer

Similar questions to practice: which-of-the-following-inequalities-has-a-solution-set-that-127820.html which-of-the-following-inequalities-has-a-solution-set-that-130666.html

bumpbot · Answer

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Which of the following inequalities have a finite range of values of x

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GMAT Problem Solving (PS) Questions

Which of the following inequalities have a finite range of values of x

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