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Mon Aug 14, 2023 2:00 am
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (01:55) correct
33%
(02:20)
wrong
based on 1975
sessions
History
Date
Time
Result
Not Attempted Yet
If a and b are, respectively, the least and greatest nonnegative real number solutions to \(|\frac{x - 6}{5}|≤ 5.5\), what is the value of b - a?
A. 11
B. 13.4
C. 27.5
D. 33.5
E. 55
A. 11
B. 13.4
C. 27.5
D. 33.5
E. 55
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Tue Aug 15, 2023 1:05 pm
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Bunuel
|(x – 6)/5| ≤ 5.5
|x – 6|/|5| ≤ 5.5
|x – 6| ≤ 27.5
Case 1: x – 6 < 0 => x < 6
-x + 6 ≤ 27.5
-21.5 ≤ x => -21.5 ≤ x < 6
Case 2: x – 6 ≥ 0 => x ≥ 6
x – 6 ≤ 27.5
x ≤ 33.5 => 6 ≤ x ≤ 33.5
After we join the solutions with “OR,” we have:
-21.5 ≤ x ≤ 33.5
Since the greatest non-negative solution is b = 33.5, and the least non-negative solution is a = 0, we have:
b – a = 33.5 – 0 = 33.5
Answer: D
Sat Jun 08, 2024 2:00 am
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Robo_123
You could represent 5.5 as 55/10; there's nothing wrong with that approach. However, without seeing your work, it's unclear how you arrived at 78/2. Here's a correct solution:
If a and b are, respectively, the least and greatest nonnegative real number solutions to \(|\frac{x - 6}{5}|≤ 5.5\), what is the value of b - a?
A. 11
B. 13.4
C. 27.5
D. 33.5
E. 55
\(|\frac{x - 6}{5}|≤ 5.5\)
\(-5.5 ≤ \frac{x - 6}{5} ≤ 5.5\)
\(-27.5 ≤ x - 6 ≤ 27.5\)
\(-21.5 ≤ x ≤ 33.5\)
\(-5.5 ≤ \frac{x - 6}{5} ≤ 5.5\)
\(-27.5 ≤ x - 6 ≤ 27.5\)
\(-21.5 ≤ x ≤ 33.5\)
The least nonnegative solution, a, is 0, and the greatest solution, b, is 33.5. Therefore, b - a = 33.5 - 0 = 33.5.
Answer: D.
Hope it helps.
