Algebra-2

To identify the absolute value inequality that generates the given graph, we analyze the inequality options provided.

From the graph, it is evident that the solution set is x ≤ 2 or x ≥ 4.

 

Analyze the Inequalities

A. 5 - 2|x - 3| ≤ 3

This translates to:
−2∣x − 3∣ ≤ −2
Dividing by −2 (which flips the inequality):

∣x − 3∣ ≥ 1

This leads to:

x - 3 ≥ 1 or x - 3 ≤ -1

 

From x - 3 ≥ 1:

x ≥ 4

 

From x - 3 ≤ -1:

x ≤ 2

The solution set is x ≤ 2 or x ≥ 4, which matches the graph.

 

B. 5 - 2|x - 3| < 3

This translates to:
−2∣x − 3∣ < −2
Dividing by −2 (which flips the inequality):

∣x − 3∣ > 1

This leads to:

x - 3 > 1 or x - 3 < -1

 

From x - 3 > 1:

x > 4

 

From x - 3 < -1:

x < 2

The solution set is x < 2 or x > 4, which does not match the graph.

 

C. 5 - 2|x - 3| > 3

This translat...