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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] New post 11 Dec 2007, 12:05
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Which of the following inequalities has a solution set that, when graphed on the number line, is a single line segment of finite length?

a) x^4 greater than or equal 1
b) x^3 less than or equal to 27
c) x^2 greater than or equal to 16
d) 2 less than or equal to |x| less than or equal to 5
e) 2 less than or equal to 3x + 4 less than or equal to 6



guys, what on earth does it mean when the graphed line segment is finite? this is the first time i encounter such a type of question and don't understand what i'm suppose to do. would appreciate your help!
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 [#permalink] New post 11 Dec 2007, 12:21
A. X is less than or equal to -1 or greater than or equal to 1. this is a split answer because everything between -1 and 1 doesn't work

B. x is less than or equal to 3. this is an infinite answer because it's all numbers below 3

C. X is less than or equal to -4 and greater than or equal to 4. another split answer that goes infinitely in either direction.

D. 2 <= |x| <= 5

x can be anywhere between 2 and 5 or -2 and -5. finite answer, but split into 2 sections.

so by process of elimination we know that E must be the answer.

E. 2 <= 3x+4 <6>= -2 and 3x<= 2

-2/3 <= x <= 2/3

finite answer in one line segment.




Answer E

EDIT: http://en.wikipedia.org/wiki/Number_line there's the wikipedia article for number line. they're looking for the equation that has all it's answers concentrated on one finite line.

so if any number over 3 is an answer it won't work because that's an infinite answer

if any number below -1 OR above 3 is an answer it won't work because there's a gap between -1 and 3.
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 [#permalink] New post 11 Dec 2007, 12:54
Expert's post
the same solution

a) x^4 greater than or equal 1 - two rays [-∞,1] and [1,+∞]
b) x^3 less than or equal to 27 - one ray [-∞,3]
c) x^2 greater than or equal to 16 - two rays [-∞,4] and [4,+∞]
d) 2 less than or equal to |x| less than or equal to 5 - two line segments [-5,-2] and [2,5]
e) 2 less than or equal to 3x + 4 less than or equal to 6 - one line segment [-2/3,2/3]
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 [#permalink] New post 11 Dec 2007, 16:03
guys, in option E, how did you get the negative sign for -2/3? also, how did you get to have both sides divided by 3? there is only one 3, so how did you manage to have both sides have the same 3? i didn't get that.
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 [#permalink] New post 11 Dec 2007, 16:05
tarek99 wrote:
guys, in option E, how did you get the negative sign for -2/3?


3x+4 is greater than or equal to 2
Subtract 4 from each side
3x is greater than or equal to -2
Divide each side by 3
x is greater than or equal to -2/3
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 [#permalink] New post 12 Dec 2007, 01:59
thanks eschn3am, so finite basically means to look for a range between 2 points without any gaps? i never knew that, and i was clueless about what i was suppose to do when i first saw this question.
  [#permalink] 12 Dec 2007, 01:59
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