Question

1. which diagram correctly shows |4|?

Explanation:

Step1: Recall absolute - value definition

The absolute value of a number \(a\), denoted as \(|a|\), is the distance of \(a\) from 0 on the number - line. For \(|4|\), it is the distance of 4 from 0 on the number - line, and the distance is 4 units.

Step2: Analyze each option

The first diagram shows a line segment from 0 to 4 with a length of 4 units, which correctly represents the distance of 4 from 0. The second diagram shows a line segment from - 4 to 0 with a length of 4 units, which represents \(|-4|\). The third diagram has two segments of length 4 units, which is not a correct representation of \(|4|\). The fourth diagram shows a line segment of length 8 units, which is incorrect for \(|4|\).

Answer:

The first diagram (the one with a line segment from 0 to 4 labeled 4 units)