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Order the numbers from least to greatest based on their absolute values: [tex]\(|23|, |-37|, |-6|, |18|, |-24|, |2|\)[/tex]

A. [tex]\(2 \ \textgreater \ 6 \ \textgreater \ 18 \ \textgreater \ 23 \ \textgreater \ 24 \ \textgreater \ 37\)[/tex]

B. [tex]\(2 \ \textless \ 6 \ \textless \ 18 \ \textless \ 23 \ \textless \ 24 \ \textless \ 37\)[/tex]

C. [tex]\(-37 \ \textgreater \ -24 \ \textgreater \ -6 \ \textgreater \ 2 \ \textgreater \ 18 \ \textgreater \ 23\)[/tex]

D. [tex]\(-37 \ \textless \ -24 \ \textless \ -6 \ \textless \ 2 \ \textless \ 18 \ \textless \ 23\)[/tex]



Answer :

GinnyAnswer
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]