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27 Sep 2025, 00:58
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
87% (01:31) correct
12% (01:52) wrong based on 16 sessions
History
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Children who ride the roller coaster must be between 24 and 52 inches tall. If \(x\) represents the height in inches of a child who may ride the roller coaster, which of the following absolute value inequalities represents all possible values of \(x\)?
A. \(| x – 24 | < 52\)
B. \(| x – 28 | < 14\)
C. \(| x – 38 | < 14\)
D. \(| x – 14 | < 38\)
E. \(| x – 28 | < 52\)
A. \(| x – 24 | < 52\)
B. \(| x – 28 | < 14\)
C. \(| x – 38 | < 14\)
D. \(| x – 14 | < 38\)
E. \(| x – 28 | < 52\)
27 Sep 2025, 01:49
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pretty easy to spot- we know that if we have mod of x- (anything) would lie between the negative of the number & the positive.
hence->
A-> 24+52 would be a lot more-> so no
B-> 28+14 is 42. so no
C-> 38+14 is 52. & also, -14+38= 24. hence we have our answer.
hence->
A-> 24+52 would be a lot more-> so no
B-> 28+14 is 42. so no
C-> 38+14 is 52. & also, -14+38= 24. hence we have our answer.
29 Sep 2025, 07:59
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Official Explanation
Find the average of 24 and 52, which is \(\frac{24+52}{2}=38\), in order to find the midpoint of 24 and 52 on a number line. The number 38 is located 14 units from both 24 and 52, so we can think of all permissible heights as those within 14 units of 38. By definition, \(|x – 38|\) means the distance from x to 38 on a number line. If we want this to be less than 14, choice (C), \(|x – 38| <14,\) properly expresses the relationship.
Answer: C
Find the average of 24 and 52, which is \(\frac{24+52}{2}=38\), in order to find the midpoint of 24 and 52 on a number line. The number 38 is located 14 units from both 24 and 52, so we can think of all permissible heights as those within 14 units of 38. By definition, \(|x – 38|\) means the distance from x to 38 on a number line. If we want this to be less than 14, choice (C), \(|x – 38| <14,\) properly expresses the relationship.
Answer: C
