Question

list the following absolute values in order from greatest to least: |-9|, -|4|, |3|, -|-5|; -|-5|, |-9|, |3|, -|4|

Explanation:

Step1: Calculate each absolute value

First, recall the definition of absolute value: the absolute value of a number \( x \), denoted \( |x| \), is the distance of \( x \) from 0 on the number line, so it is always non - negative. If there is a negative sign outside the absolute value, we calculate the absolute value first and then apply the negative sign.

• For \(|-9|\): By the definition of absolute value, \(|-9| = 9\) (since the distance of - 9 from 0 is 9).
• For \(|-4|\): The distance of - 4 from 0 is 4, so \(|-4|=4\).
• For \(|3|\): The distance of 3 from 0 is 3, so \(|3| = 3\).
• For \(-|-5|\): First, calculate \(|-5|=5\), then apply the negative sign, so \(-|-5|=-5\).

Step2: Order the values from greatest to least

Now we have the values: 9 (from \(|-9|\)), 4 (from \(|-4|\)), 3 (from \(|3|\)), and - 5 (from \(-|-5|\)).

Ordering them from greatest to least, we get \(|-9|>|-4| > |3|> -|-5|\)

Answer:

\(|-9|,|-4|,|3|,-|-5|\)