Answer :
To order the numbers [tex]\(23\)[/tex], [tex]\(-37\)[/tex], [tex]\(-6\)[/tex], [tex]\(18\)[/tex], [tex]\(-24\)[/tex], and [tex]\(2\)[/tex] from least to greatest based on their absolute values, we start by calculating the absolute value of each number:
[tex]\[ |23| = 23 \\ |-37| = 37 \\ |-6| = 6 \\ |18| = 18 \\ |-24| = 24 \\ |2| = 2 \][/tex]
Now, we list these absolute values:
[tex]\[ 23, 37, 6, 18, 24, 2 \][/tex]
Next, we sort these absolute values from least to greatest:
[tex]\[ 2, 6, 18, 23, 24, 37 \][/tex]
Thus, the numbers in ascending order based on their absolute values are:
[tex]\[ 2 < 6 < 18 < 23 < 24 < 37 \][/tex]
So, the correct answer is:
B [tex]\(\quad 2 < 6 < 18 < 23 < 24 < 37\)[/tex]
[tex]\[ |23| = 23 \\ |-37| = 37 \\ |-6| = 6 \\ |18| = 18 \\ |-24| = 24 \\ |2| = 2 \][/tex]
Now, we list these absolute values:
[tex]\[ 23, 37, 6, 18, 24, 2 \][/tex]
Next, we sort these absolute values from least to greatest:
[tex]\[ 2, 6, 18, 23, 24, 37 \][/tex]
Thus, the numbers in ascending order based on their absolute values are:
[tex]\[ 2 < 6 < 18 < 23 < 24 < 37 \][/tex]
So, the correct answer is:
B [tex]\(\quad 2 < 6 < 18 < 23 < 24 < 37\)[/tex]