Which of the following inequalities has a solution set that

Question

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

Bunuel · Accepted Answer

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)

Bunuel · Answer

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

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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

All DS Inequalities Problems to practice: search.php?search_id=tag&tag_id=184
All PS Inequalities Problems to practice: search.php?search_id=tag&tag_id=189

700+ Inequalities problems: inequality-and-absolute-value-questions-from-my-collection-86939.html

kraizada84 · Answer

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

rest of the solution sets are not finite

chris558 · Answer

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.

WholeLottaLove · Answer

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)

GMATinsight · Answer

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

ManifestDreamMBA · Answer

A. x>=4  Eliminate, no constraint on highest value 
B. x^2>=4  Eliminate, no constraint on lowest/highest value and has 2 separate lines 
C. x^3>=64  Eliminate, no constraint on highest value 
D. |x|>=4  Eliminate, splits into 2 distinct infinite lines  
E. |x|<=4 This is within a range

Which of the following inequalities has a solution set that

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