Question

the numbers -10, -4, 0, 7, and 10 are plotted on the number line.
find the absolute values.
|-10| =
|-4| =
|0| =
|7| =
|10| =
options for |10|: -10, 0, 10

Explanation:

Step1: Recall absolute value definition

The absolute value of a number \( x \), denoted \( |x| \), is the distance of \( x \) from 0 on the number line. For a negative number \( -a \) (where \( a>0 \)), \( |-a| = a \); for 0, \( |0| = 0 \); for a positive number \( a \), \( |a| = a \).

Step2: Calculate \( |-10| \)

Since -10 is negative, \( |-10| = 10 \) (distance from -10 to 0 is 10 units).

Step3: Calculate \( |-4| \)

Since -4 is negative, \( |-4| = 4 \) (distance from -4 to 0 is 4 units).

Step4: Calculate \( |0| \)

The distance from 0 to 0 is 0, so \( |0| = 0 \).

Step5: Calculate \( |7| \)

Since 7 is positive, \( |7| = 7 \) (distance from 7 to 0 is 7 units).

Step6: Calculate \( |10| \)

Since 10 is positive, \( |10| = 10 \) (distance from 10 to 0 is 10 units).

Answer:

\( |-10| = \boldsymbol{10} \)
\( |-4| = \boldsymbol{4} \)
\( |0| = \boldsymbol{0} \)
\( |7| = \boldsymbol{7} \)
\( |10| = \boldsymbol{10} \)