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Which of the following inequalities has a solution set that
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rpamecha
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Which of the following inequalities has a solution set that [#permalink] New post  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
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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.
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Bunuel
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Re: Which of the following inequalities has a solution set that [#permalink] New post  14 Apr 2012, 10:16
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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 --> this inequality clearly has one infinite solution set:
Attachment:
A..gif
A..gif [ 978 Bytes | Viewed 22425 times ]

B. x^2>=4 --> this inequality has two infinite solution sets, \(x\leq{-2}\) and \(x\geq{2}\):
Attachment:
B..gif
B..gif [ 1.02 KiB | Viewed 22416 times ]

C. x^3>=64 --> this inequality has one infinite solution set, \(x\geq{4}\):
Attachment:
C..gif
C..gif [ 978 Bytes | Viewed 22415 times ]

D. |x|>=4 --> this inequality has two infinite solution sets, \(x\leq{-4}\) and \(x\geq{4}\):
Attachment:
D..gif
D..gif [ 992 Bytes | Viewed 22409 times ]

E. |x|<=4 --> this inequality has one finite solution set, \(-4\leq{x}\leq{4}\):
Attachment:
E..gif
E..gif [ 681 Bytes | Viewed 22406 times ]


Answer: E.

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

Hope it helps.
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Re: Which of the following inequalities has a solution set...... [#permalink] New post  14 Apr 2012, 06:46
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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] New post  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] New post  17 Jun 2013, 04:51
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: Which of the following inequalities has a solution set that [#permalink] New post  01 Jul 2013, 06:59
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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

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] New post  04 Nov 2015, 09:53
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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] New post  20 Apr 2021, 02:16
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