Question

1. choose the graph that shows the inequality z < 4.4.

a: number line with 4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, open circle at 4.4, shaded left.
b: number line with 4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, open circle at 4.5, shaded left.
c: number line with 4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, open circle at 4.4, shaded right.
d: number line with 4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, open circle at 4.3, shaded right.

Explanation:

Step1: Analyze the inequality \( z < 4.4 \)

The inequality \( z < 4.4 \) means we need to represent all real numbers less than \( 4.4 \) on the number line. This should be a hollow circle (since \( 4.4 \) is not included) at \( 4.4 \) and an arrow pointing to the left (towards smaller numbers).

Step2: Evaluate each graph

• Graph A: Hollow circle at \( 4.4 \), arrow to the left (towards numbers less than \( 4.4 \)). This matches \( z < 4.4 \).
• Graph B: Hollow circle at \( 4.5 \), arrow to the left. Represents \( z < 4.5 \), not \( 4.4 \).
• Graph C: Hollow circle at \( 4.4 \), arrow to the right (towards numbers greater than \( 4.4 \)). Represents \( z > 4.4 \).
• Graph D: Hollow circle at \( 4.3 \), arrow to the right. Represents \( z > 4.3 \).

Answer:

A. The graph with a hollow circle at 4.4 and an arrow to the left (Graph A)