ccassel 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?
1. x�> 1
2. x³ ≤ 27
3. x² ≥ 16
4. 2 ≤ |x| ≤ 5
5. 2 ≤ 3x+4 ≤ 6
The equation of a line generally doesn't include exponents or absolute value.
Thus, the most linear-looking answer choice is
E:
Answer choice E: 2 ≤ 3x+4 ≤ 6
Subtract 4 from each part:
-2 ≤ 3x ≤ 2
Divide each part by 3:
-2/3 ≤ x ≤ 2/3.
-2/3 ≤ x ≤ 2/3 includes every value between -2/3 and 2/3, inclusive.
This range has two ENDPOINTS: -2/3 and 2/3.
Thus, when graphed on the number line, the solution set will yield a line segment with these two endpoints -- in other words, a line segment of FINITE LENGTH.
The correct answer is
E.
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