Which of the following inequalities has a solution set that : Problem Solving (PS)

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Which of the following inequalities has a solution set that

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Which of the following inequalities has a solution set that [#permalink]

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Updated on: 14 Apr 2012, 10:00

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Which of the following inequalities has a solution set that, when graphed on a number line, is a single, finite line segment?

A. x>=4
B. x^2>=4
C. x^3>=64
D. |x|>=4
E. |x|<=4

Spoiler: OA

Originally posted by rpamecha on 14 Apr 2012, 05:43.
Last edited by Bunuel on 14 Apr 2012, 10:00, edited 3 times in total.

Edited the question

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Re: Which of the following inequalities has a solution set that [#permalink]

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14 Apr 2012, 10:16

Which of the following inequalities has a solution set that, when graphed on a number line, is a single, finite line segment?

A. x>=4 --> this inequality clearly has one infinite solution set:

Attachment:

A..gif [ 978 Bytes | Viewed 17077 times ]

B. x^2>=4 --> this inequality has two infinite solution sets, \(x\leq{-2}\) and \(x\geq{2}\):

Attachment:

B..gif [ 1.02 KiB | Viewed 17067 times ]

C. x^3>=64 --> this inequality has one infinite solution set, \(x\geq{4}\):

Attachment:

C..gif [ 978 Bytes | Viewed 17071 times ]

D. |x|>=4 --> this inequality has two infinite solution sets, \(x\leq{-4}\) and \(x\geq{4}\):

Attachment:

D..gif [ 992 Bytes | Viewed 17065 times ]

E. |x|<=4 --> this inequality has one finite solution set, \(-4\leq{x}\leq{4}\):

Attachment:

E..gif [ 681 Bytes | Viewed 17066 times ]

Answer: E.

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

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Re: Which of the following inequalities has a solution set...... [#permalink]

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14 Apr 2012, 06:46

rpamecha wrote:

Which of the following inequalities has a solution set that, when graphed on a number line, is a single, finite line segment?

1) x>=4
2) x^2>=4
3) x^3>=64
4) |x|>=4
5) |x|<=4

Please explain your answer.

OA to follow, after some discussion.

its 5).
-4 <= x<= 4

rest of the solution sets are not finite
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Re: Which of the following inequalities has a solution set that [#permalink]

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27 Jun 2012, 10:36

rpamecha wrote:

Which of the following inequalities has a solution set that, when graphed on a number line, is a single, finite line segment?

A. x>=4
B. x^2>=4
C. x^3>=64
D. |x|>=4
E. |x|<=4

The best way to solve this problem is to do so using number lines.
a) Infinite
b) |x|>=2 which means x>=2 and x<=-2. Infinitite in opposite directions.
c) x>=4 Infinite
d) x>=4 and x<=-1 Infinite in opposite directions
e) x<=4 and x>=-4 which means -4<=x<=4. !!!

The answer is E.

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Re: Which of the following inequalities has a solution set that [#permalink]

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17 Jun 2013, 04:51

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html
everything-is-less-than-zero-108884.html
graphic-approach-to-problems-with-inequalities-68037.html

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Re: Which of the following inequalities has a solution set that [#permalink]

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01 Jul 2013, 06:59

Which of the following inequalities has a solution set that, when graphed on a number line, is a single, finite line segment?

A. x>=4
B. x^2>=4
C. x^3>=64
D. |x|>=4
E. |x|<=4

Running through the list, it's pretty easy to rule out A, B, C

Let's try D
|x|>=4

x≥4
OR
-x≥4 ===> x≤-4
In other words, x may be greater than four (going from left to infinity on the number line) or it could be less than negative four (going from right to negative infinity on the number line)
INCORRECT

|x|<=4
x≤4
-x≤4 ===> x≥-4

So:
-4≤x≤4
In other words, x could be between -4 and 4 on the number line.

(E)

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Which of the following inequalities has a solution set that [#permalink]

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04 Nov 2015, 09:53

rpamecha wrote:

Which of the following inequalities has a solution set that, when graphed on a number line, is a single, finite line segment?

A. x>=4
B. x^2>=4
C. x^3>=64
D. |x|>=4
E. |x|<=4

Checking Options:

A. x>=4 i.e. Single Line segment of Infinite length to the right of 4 on Number Line

B. x^2>=4 i.e. x>=2 or x <=-2 i.e. Two Line segment of Infinite length to the right of 2 and to the left of -2 on Number Line

C. x^3>=64 i.e. x >=4 i.e. Single Line segment of Infinite length to the right of 4 unit on Number Line

D. |x|>=4 i.e. x >=4 or x <=-4 i.e. Two Line segments of Infinite length to the right of 4 and left of -4 on Number Line

E. |x|<=4 i.e. Single Line segment of FINITE length from -4 to +4 on Number Line with length of 8 units

Answer: option E
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Re: Which of the following inequalities has a solution set that [#permalink]

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19 Jan 2018, 06:00

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