Question

complete the statements.
-7 and 7 both have an absolute value of?
the distance between -2 and 5 is? units.

Explanation:

First Statement:

Step1: Recall absolute value definition

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

Step2: Calculate \( |-7| \) and \( |7| \)

For \( -7 \), \( |-7| = 7 \) (since distance from 0 is 7). For \( 7 \), \( |7| = 7 \) (distance from 0 is 7). So both have absolute value 7.

Second Statement:

Step1: Recall distance formula on number line

The distance between two numbers \( a \) and \( b \) is \( |a - b| \) (or \( |b - a| \), since absolute value is symmetric).

Step2: Apply formula to -2 and 5

Let \( a = -2 \) and \( b = 5 \). Then distance is \( |5 - (-2)| = |5 + 2| = |7| = 7 \).

Answer:

First blank: 7
Second blank: 7