Which of the following numbers is closest to 7 on a number line: Absolute value of 4, Absolute Value 5, Absolute value of 9, Absolute value of -6?
Understand the Problem
The question asks to determine which of the given absolute values results in a number closest to 7 on a number line. This involves calculating the absolute value of each option and then comparing the results to 7 to find the smallest difference.
Answer
$|3-11|$, $|-4-2|$, and $|-1-5|$
Answer for screen readers
$|3-11|$, $|-4-2|$, and $|-1-5|$ are all equally close to 7.
Steps to Solve
- Evaluate the absolute value of each option
Evaluate $|3-11|$: $|3-11| = |-8| = 8$
Evaluate $|-4-2|$: $|-4-2| = |-6| = 6$
Evaluate $|-1-5|$: $|-1-5| = |-6| = 6$
Evaluate $|-2-12|$: $|-2-12| = |-14| = 14$
- Find the difference between each result and 7
Find the difference between 8 and 7: $|8-7| = 1$
Find the difference between 6 and 7: $|6-7| = |-1| = 1$
Find the difference between 6 and 7: $|6-7| = |-1| = 1$
Find the difference between 14 and 7: $|14-7| = 7$
- Identify the smallest difference
The smallest differences are 1, 1, and 1, which correspond to the first three options.
- Determine which options result in the smallest difference
Since options $|3-11|$, $|-4-2|$, and $|-1-5|$ each have a difference of 1 from 7, they are all equally close to 7.
$|3-11|$, $|-4-2|$, and $|-1-5|$ are all equally close to 7.
More Information
All options $|3-11|$, $|-4-2|$, and $|-1-5|$ are the same distance (1 unit) away from 7 on the number line.
Tips
A common mistake is to incorrectly evaluate the absolute value expressions, especially when dealing with negative numbers. For example, incorrectly calculating $|-4-2|$ as $|-4| - |2| = 4 - 2 = 2$ instead of $|-6| = 6$. Another mistake is to compare the absolute values directly without finding the difference from 7.
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