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

\(A. x^4 ≥ 1\)

\(B. x^3 ≤ 27\)

\(C. x^2 ≥ 16\)

\(D. 2≤ |x| ≤ 5\)

\(E. 2 ≤ 3x+4 ≤ 6\)

Lets check one by one

\(x^4 ≥ 1\)

Nope :- This maps to a two value of x≥1 and x ≤-1 on the number line. This is the not a finite line. This is actually an infinite line broken only from -1 to 1 but extending from

-∞ to

+∞\(x^3 ≤ 27\)

Nope:- This maps to infinite values of ≤3 on the number line. This is the equation of a INFINITE line from 3 to

-∞\(x^2 ≥ 16\)

Nope :- This maps to a two value of x≥4 and x ≤-4 on the number line. This is the not a finite line. This is actually an infinite line broken only from -4 to 4 but otherwise extending from

-∞ to

+∞\(2≤ |x| ≤ 5\)

Looks interesting. Lets check |X| can actually be seen as +x and also =-x

Lets check both cases individually

CASE 1) \(2≤ x≤ 5\) This gives a finite line.

CASE 2) \(2≤ -x ≤ 5\) or\(-5≤ x ≤ -2\)This gives a finite line again

A TOTAL OF 2 FINITE RANGES. We need only one finite range.

\(2 ≤ 3x+4 ≤ 6\)

\(x≥-\frac{2}{3}\) and \(x≤\frac{2}{3}\) or \(-\frac{2}{3}≤x≤\frac{2}{3}\)

YES this is a finite range from -x to +x

E IS THE ANSWER

≥ ≤ ∞

dvinoth86 wrote:

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 ≥ 1

B. x^3 ≤ 27

C. x^2 ≥ 16

D. 2≤ |x| ≤ 5

E. 2 ≤ 3x+4 ≤ 6

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