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:
B. x^2>=4 --> this inequality has two infinite solution sets, \(x\leq{-2}\) and \(x\geq{2}\):
C. x^3>=64 --> this inequality has one infinite solution set, \(x\geq{4}\):
D. |x|>=4 --> this inequality has two infinite solution sets, \(x\leq{-4}\) and \(x\geq{4}\):
E. |x|<=4 --> this inequality has one finite solution set, \(-4\leq{x}\leq{4}\):

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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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.

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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